Curriculum Vitae

Jian-Guo Liu

Box 90320, Durham, NC 27708-0320 (919) 660-2546 (office)
(email)
Education

Ph.D.University of California - Los Angeles1990
M.S.Fudan University (China)1985
B.S.Fudan University (China)1982
Areas of Research

Applied Mathematics, Nonlinear Partial Differential Equations.

Areas of Interest

Collective dynamics, decision making and self-organization in complex systems coming from biology and social sciences,
Scaling behavior in models of clustering and coarsening,
Numerical methods for incompressible viscous flow,
Multiscale Analysis and Computation

Professional Experience / Employment History

Duke University
Professor, Department of Physics and Department of Mathematics, 2009 - present
University of Maryland, College Park
Professor, Department of Mathematics and Institute for Physical Science and Technology, 2001 - 2009
Associate Professor, Department of Mathematics and Institute for Physical Science and Technology, 1997 - 2001
Institute for Advanced Study
Member, January, 1994 - August, 1994
Temple University
Assistant Professor, Department of Mathematics, 1993 - 1997
New York University
Courant Instructor/Visiting Member, Courant Institute of Mathematical Sciences, 1991 - 1993
Mathematical Sciences Research Institute
Postdoctoral Fellow, 1990 - 1991
Visiting Positions
Visiting Member, New York University, 1996 - 1997
Awards, Honors, and Distinctions

Jian-Guo Liu and Bob Pego, ICCM – International Consortium of Chinese Mathematicians, December, 2020
Recent Grant Support

Conferences Organized

Organized with Jianfeng Lu a conference Collective Dynamics in Biological and Social Systems, Nov 19 - 22, 2015  
Co-organized SIAM Conference on Analysis of Partial Differential Equations, mini-symposium: Asymptotically Preserving Numerical Methods for Time-Depe, December 2013  
Organizer Committee : IMA Workshop on Analysis and Computation of Incompressible Fluid Flow, Organizer Committee : IMA Workshop on Analysis and Computation of Incompressible Fluid Flow. February 2010, February, 2010  
Organizer Committee, Singapore : Two Month Program on Mathematical Theory and Numerical Methods for Computational Materials Simulation and Design, Organizer Committee, Singapore : Two Month Program on Mathematical Theory and Numerical Methods for Computational Materials Simulation and Design. Jul, July, 2009 - August, 2009  
Co-Chair, "Twelfth International Conference on Hyperbolic Problems Theory, Numerics, Applications'', Maryland, June, 2008  
Organizer Committee, Maryland, CSCAMM Workshop on Analytical and Computational Challenges of Incompressible Flows at High Reynolds Number, October 23, 2006 - October 26, 2006  
Organizing Committee, Singapore, The Nonlinear Partial Differential Equations: Analysis, Numerics and Applications, May, 2005  
Co-Chair, Singapore, Two month program on ``Nanoscale Material Interfaces: Experiment, Theory and Simulation'', November 24, 2004 - January 23, 2005  
Co-Chair, First Singapore Workshop on PDE and Scientific Computing, December, 2004  
Professional Service

A&S Council
Served on dissertation committee for Yuantong Ding, Department of Biology, 2014 - present  
Prelim exam committee for Qiang Ren, Department of Electrical and Computer Engineering, December 2014  
Dept Committee
Prelim committee for Charlio Xu, Mathematics, 2015, 2015 - present  
Prelim committee for Qingtao Sun, Department of Electrical and Computer Engineering, 2015 - present  
Advising Math Major for Yi Chen, 2015 - present  
Advising Math Major for Daniel Ye Zhu, 2015 - present  
Advising Math Major for Yuzhe Shi, 2015 - present  
Chair, committee to revamp the Mathematics departments Numerics Classes, 2015 - present  
Chair, mentoring committee for Barthel, 2015 - present  
ARP appointment committee, Department of Mathematics, 2015 - present  
Chair, Physics Computing Committee, 2015 - present  
Advising Math Major for Mandy Ruigi Jiang, 2014 - present  
Advising Math Major for Duke Kyeom Kim, 2014 - present  
Prelim committee for Hangjie Ji, 1 July 2014  
Member of Physics core course committee, 2013 - present  
Member of Physics Undergraduate Curriculum Committee, 2013 - present  
Math Mentoring, September 1, 2012 - present  
Major advising, January 6, 2012 - present  
Reappointment Committee for Lu, Department of Mathematics, December 2015  
Appointment Committee for Mayboroda, Department of Mathematics, December 2015  
Ph.D. dissertation committee for Ethan Elliott, December 2014  
Ph.D. dissertation committee for Di-Lun Yang, September 1, 2011 - 2014  
Preliminary examination committee for Joey Schmitt, December 2013  
Math honors theses advising for Kara Karpman, December 2013  
Ph.D. defense committee for Luis Tobon, December 2013  
Prepare and grade the assessment exam for Thermal Physics, December 2013  
Graduate assessment committee, Physics, 2011 - 2013  
Ph.D. dissertation committee for Huaixiu Zheng, January 13, 2011 - 2013  
Thesis Defense Committee for Yi Li, November 27, 2012  
Written Analysis Qual Exam Committee, September 1, 2010 - August 31, 2012  
Oral qualifying exam committee for Jingxian Huang, May 5, 2012  
Ph.D. dissertation committee for Chingyun Cheng, March 5, 2012 - 2012  
Preliminary Examination Committee for Chingyun Cheng, Physics, December 2011  
Thesis Defense Committee for Matt Bowen, Mathematics, November 2011  
Chair for Committee to Review Prof. Jim Nolen, Mathematics, November 2011  
Committee to Review Prof. Steffen Bass, Physics, November 2011  
Preliminary Examination Committee for Yi Li, Mathematics, 2010  
Chair, Physics Computing Committee, 2009 - 2010  
ARP committee, December 2009  
Committee for Preliminary Exam for Jiefu Chen, Dept of Electrical and Computer Engineering, November 18, 2009  
Papers Refereed
Served on exterior doctoral committee for Jeff Eisenbesis, Carnegie Mellon University, 2014 - present  
Served on exterior doctoral committee for Wang Nan, National University of Singapore, 2014 - present  
Co-organized SIAM PDE13 mini-symposium: Asymptotically Preserving Numerical Methods for Time-Dependent PDEs, Co-organized SIAM PDE13 mini-symposium: Asymptotically Preserving Numerical Methods for Time-Dependent PDEs. December 22, 2013, 22 December 2013  
Member of the Steering Committee for the Tsinghua Sanya International Mathematics Forum, Member of the Steering Committee for the Tsinghua Sanya International Mathematics Forum. 2013, 2013 - present  
Refereed for a number of journals, Refereed for a number of journals. 2013, 2013 - present  
Member of the Steering Committee for the Tsinghua Sanya International Mathematics Forum, Member of the Steering Committee for the Tsinghua Sanya International Mathematics Forum. 2013, 1 January 2013  
Refereed for a number of journals, Refereed for a number of journals. 2013, 1 January 2013  
Panelist for Yau High School Mathematics Award, 2014  
exterior doctoral committee for Baver Okutmustur, University Paris VI, exterior doctoral committee for Baver Okutmustur, University Paris VI. 2010, 2010  
Served on Panel: National Science Foundation, CFD, 2007, December 2007  
NSF Reviews And Panels
panelist : NSF Numerical Methods (P100833) panel, panelist : NSF Numerical Methods (P100833) panel. March 2010, March, 2010  
Math Community Services
Associated editor for Annals of Mathematical Sciences and Applications, 2015 - present  
Promotion and tenure external evaluators for various universities, Promotion and tenure external evaluators for various universities. July 1, 2012, 1 July 2012  
Managing Editor, "Methods and Applications of Analysis'', 2007 - present  
Managing Editor for "Journal of Hyperbolic Differential Equations'', 2004 - present  
Editorial Board for "Applied Mathematics--A Journal of Chinese Universities'', 2003 - present  
Tutorial Lectures for Program: "Partial Differential Equations in Kinetic Theories", Newton Institute, Cambridge, UK, Tutorial Lectures for Program: "Partial Differential Equations in Kinetic Theories", Newton Institute, Cambridge, UK. August 2010 - September 2010, August-September, 2010  
Editorial Board, "Journal of Information and Computational Science'', 2005 - 2008  
Univ Services
Initialed and signed a MOU between The Math department at Duke and the Mathematical Science Center (MSC), Tsinghua University, July 1, 2013  
Selected Recent Invited Talks

Macroscopic Dynamics for Nonequilibrium Biochemical Reactions from A Hamiltonian Viewpoint, Seminars in Mathematical Biology, SJTU, 25 December 2021  
Stochastic and PDE models for neuron networks: justification and numerical simulation, Mathematics in Action (MiA2021): Modeling and analysis in molecular biology and electrophysiology, 25 December 2021  
Random batch method for interacting particle systems and mean field limit, The Institute for Mathematical and Statistical Innovation (IMSI), November 3, 2021  
Contact line dynamics for merging and splitting of droplets: gradient flow formulation and computations, Dec 27-29  
Data-driven solvers and optimal control for conformational transitions based on high dimensional point clouds with manifold structure, September 24, 2020  
Rigorous justification of Fokker-Planck equations of neural networks based on an iteration perspective, May 24, 2020  
Data-driven efficient solvers and predictions of conformational transitions for Langevin dynamics on manifold in high dimensions, March 29, 2020  
Random batch methods (RBM) for large interacting particle systems, Illinois Institute of Technology, September 15, 2019  
Random Batch Method and its application to sampling,, US Census Bureau, August 27, 2019  
Well-posedness and derivative blow-up for a dispersionless regularized shallow water system, University California, San Diego, May 30, 2019  
Least action principle for incompressible flow with free boundary, Fudan University, Shanghai, March 22, 2019  
Least action principle for incompressible flow with free boundary, East China Normal University, Shanghai, 15 March 2019  
Dynamics of a degenerate PDE model of epitaxial crystal growth, Beijing, June 9-14, 2019  
Merging-splitting dynamics for animal group size without detailed balanc, Shanghai Jiao Tong University, April 8-9, 2019  
Numerical Methods for some Nonlinear Transport Equations in Biology, Southern University of Science and Technology, China, Nov 2-4, 2019  
Peierls-Nabarro model for single edge dislocation: mathematical validation and exponential convergence to equilibrium, Northwest University, Xi’an, China,, June 28 -30, 2019  
Random batch methods (RBM) for large interacting particle systems, Richmond, VA, Oct 10 - 13, 2019  
An analysis of merging-splitting group dynamics by Bernstein function theory, Invited talk at conference: Analysis and Computation in Kinetic Theory, Stanford University, Nov 2-6, 2015  
An analysis of merging-splitting group dynamics by Bernstein function theory, Invited talk at conference: Frontiers of Applied and Computational Mathematics, Celebrating Professor Björn Engquist's 70th Birthday, Peking University, China, Aug 7-9, 2015  
An analysis of merging-splitting group dynamics by Bernstein function theory, Invited talk at conference: International Conference on Numerical Partial Differential Equations and Their Applications, Wuhan University, China, May 25-29, 2015  
Euler sprays and optimal transportation, Invited talk at conference: Particle Systems and Partial Differential Equations IV, University of Minho, Braga, Portugal, Dec 16-18, 2015  
Multi-scale hyperbolic relaxation system, kinetic-fluid domain coupling, and singular limit analysis, Invited talk at conference: Asymptotic Preserving and Multiscale Methods for Kinetic and Hyperbolic Problems, University of Wisconsin-Madison, May 4-9, 2015  
Particle, kinetic, and hydrodynamic models of swarming and network traffic models, Invited talk at conference: Groups and interactions in data, networks and biology, Carnegie Mellon University, May 27-29 2015  
Stability of micro-macro decomposition base stochastic Galerkin method for linear transport equation with random inputs and diffusive scalings, Invited talk at conference: Uncertainty quantification in kinetic and hyperbolic problems, University of Wisconsin-Madison, Mar 28 - 31, 2015  
An analysis of merging-splitting group dynamics by Bernstein function theory, Colloquium, Indiana University, October 23, 2015  
Phase transitions and hysteresis for self-organized alignment dynamics, Lefschetz Center for Dynamical Systems Seminar, Brown University, March 02, 2015  
Particle Systems and Partial Differential Equations III, the University of Minho in Braga, Portugal, December, 2014  
An analysis of merging-splitting group dynamics by Bernstein function theory, Northeast Normal University, China, July 28, 2014  
An analysis of merging-splitting group dynamics by Bernstein function theory, Fudan University, China, July 21, 2014  
An analysis of merging-splitting group dynamics by Bernstein function theory, 4th Beijing Normal University-PDE Workshop, July, 2014  
A kinetic mean field game theory for the evolution of wealth, USA Census Bureau, May 13, 2014  
A kinetic mean field game theory for the evolution of wealth, Principal lecturer, Dynamics and Numerics for Non-local PDEs and Related Equations in the Physical and Biological Sciences, NSF-supported Ki-Net Summer School, Iowa State University, May, 2014  
Kinetics, non standard diffusion and stochastics: emerging challenges in the sciences, Austin, May, 2014  
Phase transitions and hysteresis for self-organized alignment dynamics 1 & 2, Principal lecturer, NSF-supported Ki-Net Summer School, Iowa State University, May, 2014  
An analysis of merging-splitting group dynamics by Bernstein function theory, ``Modern Perspectives in Applied Mathematics: Theory and Numerics of PDEs'', Maryland, April, 2014  
Well-posedness and singular limit of a semilinear hyperbolic relaxation system with a two-scale discontinuous relaxation rate, ``Asymptotic-Preserving Schemes for Multiscale Kinetic Equations" NCSU, February, 2014  
Coagulation-Fragmentation model without detailed balance for animal group-size statistics, CSCAMM/KI-Net Seminar, University of Maryland, September 11, 2013  
Coagulation-Fragmentation model without detailed balance for animal group-size statistics, Academia Sinica, China, August 08, 2013  
Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics, 11th workshop on nonlinear PDE, Beijing University of Technology, August, 2013  
The dynamic and steady states for multi-dimensional Keller-Segel model with the diffusion exponent m > 0, Northeast Normal University, Changchun, China, July 26, 2013  
Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics, Seminar of the Institute of Mathematics, Peking University, July 15, 2013  
Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics, Séminaire de l’équipe MIP, Institut de Mathématiques de Toulouse, Université Paul Sabatier, June 25, 2013  
Global weak solution for kinetic models of active swimming and passive suspensions, The International Conference on Mathematical Modeling and Computation (ICMMC2013), Wuhan Univeristy, May, 2013  
The dynamic and steady states for multi-dimensional Keller-Segel model with the diffusion exponent m>0, PDE seminar, University of Maryland, February 21, 2013  
Phase transitions for self-organized dynamics and sweeping networks, conference on "Transport Models for Collective Dynamics in Biological Systems", NCSU, January, 2013  
Estimate on Laplace-Leray commutator and application to the Navier-Stokes equation in a bounded domain, Seminar, CEREMADE, Université de Paris, Dauphine, France, December 11, 2012  
Phase transition for Smoluchowski equation, Seminar, University of Rennes, France, 22 November 2012  
Global weak solution for kinetic models of active swimming and passive suspensions, seminar of Applied Maths of the Institut de Mathematiques de Toulouse, France, October 09, 2012  
Phase transition of self-alignment in flocking dynamics, "Applied Partial Differential Equations in Physics, Biology and Social Sciences: Classical and Modern Perspectives'', Bellaterra, Spain, September 07, 2012  
Multi-dimensional Keller-Segel model with supercritical diffusion exponent, "2012 International Conference on Applied Mathematics'', Morningside Center of Mathematics, China, August 07, 2012  
Multi-dimensional Keller-Segel model with supercritical diffusion exponent, "One-day workshop on mathematical topics of fluid dynamics'', Academia Sinica, China, July 17, 2012  
Viscek flocking dynamics and phase transition, "14th International Conference on Hyperbolic Problems: Theory, Numerics, Applications'', Università di Padova, Italy, June 28, 2012  
Bacterium swimming, flocking dynamics and phase transition, Math Literature Seminar, Tsinghua, China, June 27, 2012  
Mathematical analysis of flocking dynamics in biology and social science, USA Census Bureau, June 19, 2012  
Convergence of a Particle Method and Global Weak Solutions for a Family of Evolutionary PDEs, Applied and Numerical Analysis Seminar, University of Crete, Greece, December 15, 2011  
Asymptotic-Preserving schemes for kinetic–fluid modeling of disperse two-phase flows, Applied and Numerical Analysis Seminar, University of Crete, Greece, December 8, 2011  
Global weak solution for kinetic models of active swimming and passive suspensions, Colloquium of the Department of Applied Mathematics, University of Crete, Heraklion, Greece, November 23, 2011  
Dynamics of orientational alignment and phase transition, Colloquium, Department of Mathematics, Tulane university, October 20, 2011  
Pressure boundary condition and projection method, "Modern Techniques in the Numerical Solution of Partial Differential Equations'', Crete, Greece, September, 2011  
Hydrodynamics of Vicsek self-alignment interactions, colloquium, Capital Normal University, August 2, 2011  
Multi-dimensional degenerate Keller-Segel system with critical diffusion exponent 2n/(n+2), "International Conference on Applied Mathematics and Statistics'', Renmin University, Beijing, August, 2011  
Hydrodynamics of self-alignment interactions with precession and derivation of the Landau-Lifschitz-Gilbert equation, Applied math Seminar, Shanghai Jiao Tong University, July 13, 2011  
Dynamics of orientational alignment and phase transition, International Conference on Applied and Computational Mathematics and Interdisciplinary Research, Nankai University, June, 2011  
Dynamics of orientational alignment and phase transition, CSCAMM seminar, University of Maryland, April 20, 2011  
Dynamics of orientational alignment and phase transition, Numerical Methods for PDEs seminar, MIT, April 6, 2011  
Dynamics of orientational alignment and phase transition, Colloquium, Georgetown University, February 11, 2011  
Dynamics of orientational alignment and phase transition, workshop on "Pedestrian Traffic Flow", SAMSI, NC, February, 2011  
Asymptotic-preserving schemes for some kinetic equations, Workshop on "Numerical Methods for stiff problems in Hamiltonian systems and kinetic equations", Saint-Malo, France, January, 2011  
Dynamics of orientational alignment and phase transition, Fifth International Congress of Chinese Mathematicians, Beijing, China, December, 2010  
Modeling and analysis of collective behavior of self-propelled agents, Colloquium, Beijing University of Posts and Telecommunications, December 1, 2010  
Dynamics of orientational alignment and phase transition, Colloquium, Tsinghua University,China, November 18, 2010  
Dynamics of orientational alignment and phase transition, Seminar, Huazhong Normal University, CHina, November 12, 2010  
Estimate on commutator of the Laplacian and Leray projection operators and application to Navier-Stokes equation in bounded domain, Colloquium, Wuhan University, China, November 12, 2010  
Modeling and analysis of collective behavior of self-propelled agents, Seminar, Huazhong University of Science and Technology, November 11, 2010  
Dynamics of orientational alignment and phase transition, Conference on Nonlinear PDEs, Beijing University of Technology, China, November, 2010  
Modeling and analysis of collective behavior of self-propelled agents, Colloquium, Capital Normal University, Beijing, October 19, 2010  
Dynamics of orientational alignment and phase transition, 2010 NIMS Thematic Program Workshop on Conservation Laws, Plasma and Related Fields, Seoul National University, South Korea, October, 2010  
Analysis of dynamics of Doi-Onsager phase transition, Colloquium, Institute of Mathematics, Chinese Academy of Sciences, September 29, 2010  
Analysis of Dynamics of Doi-Onsager Phase Transition, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, September 6, 2010  
Estimate on commutator of the Laplacian and Leray projection operators and application to Navier-Stokes equation in bounded domain, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, September 3, 2010  
Asymptotic-preserving schemes for some kinetic equations, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, August 31, 2010  
Some estimates on collective behavior of self-propelled biological agents, Marketplace of Ideas, Center for Theoretical and Mathematical Science, Duke University, December 3, 2009  
Asymptotic-preserving schemes for fluids equations and kinetic equations, Numerical Analysis Seminar, North Carolina State University, November 17, 2009  
Modeling and analysis of collective behavior of self-propelled agents, Applied Mathematics Seminar, Tulane university, November 6, 2009  
The challenge of simulating fluid flow accurately in the presence of boundaries, Colloquium, Tulane University, November 5, 2009  
Analysis and computation of Navier–Stokes equation in bounded domains, Applied and Computational Analysis Seminar, University of Cambridge, UK, October 5, 2009  
Modeling and analysis of collective behavior of self-propelled agents, Applied Math & PDE Seminar, University of Wisconsin, Madison, September 4, 2009  
Controlling numerical dissipation and time stepping in some multi-scale kinetic/fluid simulations, CSCAMM Workshop on Kinetic Description of Multiscale Phenomena, Maryland, September, 2009  
Modeling and analysis of collective behavior of self-propelled agents, Colloquium, National University of Singapore, August 19, 2009  
Some numerical analysis issues in material and fluids simulations, Workshop on Mathematical Theory and Computational Methods in Materials Sciences, IMS/NUS, Singapore, August, 2009  
A simple proof of the Cucker-Smale flocking dynamics and mean-field limit, ICMS Workshop on Kinetic and Mean-field models in the Socio-Economic Sciences, Edinburgh, UK,, July, 2009  
A simple proof of the Cucker-Smale flocking dynamics and mean-field limit, Workshop on Kinetics and statistical methods for complex particle systems, Lisbon, Portugal, July, 2009  
Asymptotic-preserving schemes for fluids equations and kinetic equations, Seminaire Methodes Numeriques pour les problemes hyperboliques, Universite Pierre et Marie Curie, France,, June 9, 2009  
The challenge of simulating fluid flow accurately in the presence of boundaries, groupe de travail, Universités Paul Sabatier, France, June 8, 2009  
Pressure and projection methods for viscous incompressible flows, PDE seminar, Oxford University, UK, May 11, 2009  
A new approach in analysis and computation of Navier-Stokes equation in bounded domain, Scientific Computing - Numerical Analysis Seminar, Universite Bordeaux 1, France, March 12, 2009  
The challenge of simulating incompressible fluid flow accurately in the presence of boundaries, Colloquium, Department of Mathematics, Howard University, January 30, 2009  
All speed asymptotic-preserving schemes for compressible flows, Recent Developments in Numerical Methods for Nonlinear Hyperbolic Partial Differential Equations and their Applications, Banff Int'l Research Station for Math Innovation and Discovery, Canada, August, 2008  
A simple proof of Cucker-Smale flocking dynamics and the mean field limit, Applied Math Seminar, National Taiwan University, Taiwan, July 25, 2008  
A simple proof of Cucker-Smale flocking dynamics and the mean field limit}, Applied and Computational Math Seminar, National Tsing Hua University, Taiwan, July 24, 2008  
Mach number uniform asymptotic preserving schemes for fluids and plasmas, Seminar on Applied Mathematics, Inst. of Math., Academia Sinica, Taiwan, July 14, 2008  
The challenge of simulating incompressible fluid flow accurately in the presence of boundaries, Applied and Computational Mathematics Seminar, UNC Charlotte, May 9, 2008  
The challenge of simulating incompressible fluid flow accurately in the presence of boundaries, Physics Colloquium, Duke University, May 6, 2008  
A simple proof of the Cucker-Smale flocking dynamics and mean-field limit,, AMS regional meeting, mini-symposium: "Special Session on Numerical Solution of Partial Differential Equations and Applications", NCSU, April, 2008  
Computation of incompressible flow past a sphere and local behavior of boundary layer separation, CNCS Seminar, Duke University, April 1, 2008  
A simple proof of Cucker-Smale flocking dynamics and the mean field limit, Brown Bag seminar, Duke University, March 21, 2008  
On computation of incompressible flow past a sphere, Seminaire du laboratoire, Laboratoire MIP, Universite Paul Sabatier, Toulouse, France, March 10, 2008  
Finite element Navier-Stokes solvers based on an unconstrained reformulation, Applied Math Seminar, University of Delaware, Newark, March 4, 2008  
Finite element Navier-Stokes solvers based on an unconstrained reformulation, Applied Math & PDE Seminar, University of Wisconsin, Madison, February 22, 2008  
Characterization and regularity of symmetric solenoidal vector fields with application to Navier-Stokes equation, Fourth International Congress of Chinese Mathematicians, Hangzhou, China, December, 2007  
Macroscopic fluid models with localized kinetic upscaling effects , Workshop on Quantized vortices in superfluidity and superconductivity and kinetic theory, National University of Singapore, December, 2007  
Estimate on Laplace-Leary commutators and application to Navier- Stokes equation, International Conference on Applied Partial Differential Equations, East China Normal University, July, 2007  
Characterization and Regularity of Symmetric Solenoidal Vector Fields with Application to Navier-Stokes Equation, IMS Seminar, The Chinese University of Hong Kong, June 28, 2007  
Approximate projection operator, Uzawa iteration, sequential regularization and Navier-Stokes solver, Seminar in Applied Math, National Center for Theoretical Sciences, Taiwan, June 20, 2007  
Estimate on Laplace-Leary commutators and application to Navier-Stokes equation, Seminar on Applied Mathematics, Inst. of Math., Academia Sinica, Taiwan, June 18, 2007  
No-slip Navier-Stokes solvers built with Laplace-Leray commutators, Applied Math Seminar, National Chiao Tung University, Taiwan, June 15, 2007  
Asymptotic preserving Gauge schemes for transitional Mach number flows, Seminar in Scientific Computation, National Center for Theoretical Sciences, Taiwan, June 14, 2007  
Fluid models with localized kinetic upscaling, Applied Math Seminar, National Taiwan University, June 6, 2007  
On incompressible Navier-Stokes dynamics: a new approach for analysis and computation, The second MINNHOKEE memorial lecturer, Seoul National University, May, 2007  
On incompressible Navier-Stokes dynamics: a new approach for analysis and computation, Second Workshop on Nonlinear Partial Differential Equations: Analysis, Numerics and Applications, Seoul National University, May, 2007  
Incompressible Navier-Stokes equation: theory and computation II, Special Seminar, Seoul National University, South Korea, April 29, 2007  
Incompressible Navier-Stokes Equation: Theory and Computation I, Special Seminar, Seoul National University, April 28, 2007  
Efficient formulation of Navier-Stokes Equation and computation, Applied Math Seminar, Duke University, February 5, 2007  
A new approach for analysis and computation of Navier-Stokes Equation in bounded domains, Applied Math Colloquium, University of North-Carolina at Chapel Hill, December 1, 2006  
Pressure estimate for the incompressible Navier-Stokes equation in a bounded domain, Differential Equations Seminar, North Carolina State University, Raleigh, November 15, 2006  
Pressure estimates for Navier-Stokes equation in bounded domain, Applied Math Seminar, Michigan State University, November 07, 2006  
Pressure estimates for Navier-Stokes equation in bounded domain, PDE Seminar, Georgia Institute of Technology, October 10, 2006  
Pressure estimate for the incompressible Navier-Stokes equation in a bounded domain, CSCAMM Workshop on Analytical and Computational Challenges of Incompressible Flows at High Reynolds Number, Maryland, October, 2006  
A new pressure estimate for the incompressible Navier-Stokes equations in a bounded domain, Mathematical Analysis and Applications Seminar, Weizmann Institute of Science, Israel, August 08, 2006  
Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate, Seminar in Applied Mathematics, Hebrew University Jerusalem, Israel, July 31, 2006  
Incompressible Navier-Stokes dynamics in bounded domains---a new approach for analysis and computation, Numerical Analysis Seminar, Tel Aviv University, Israel, July 30, 2006  
Mathematical modellings and numerical methods for multi-scale problems I & II, School on Modern Numerical Methods in Math and Physics", NCTS, Taiwan, July, 2006  
On incompressible Navier-Stokes dynamics: a new approach for analysis and computation, NCTS International Workshop on Scientific Computing, Taiwan, June, 2006  
Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate, Frontiers in Applied and Computational Mathematics, New Jersey Institute of Technology, May, 2006  
Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate, Numerical Analysis and Math Physics Seminar, University of North Carolina at Charlotte, April 18, 2006  
Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate, Kyoto Conference on the Navier-Stokes equations and their Applications , Kyoto, Japan, January, 2006  
Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate, PDE Seminar, Northwestern University, November 17, 2005  
Divorcing pressure from viscosity in computing incompressible Navier-Stokes dynamics in bounded domains, CAMP/Nonlinear PDE's Seminar, University of Chicago, November 16, 2005  
Finite Element Navier-Stokes Solvers without Inf-Sup Conditions, Colloquium, University of Maryland, Baltimore County, September 16, 2005  
Novel Finite Element Navier-Stokes Solvers without Inf-Sup Conditions, Numerical Analysis Seminar, University of Maryland, College park, September 06, 2005  
Divorcing pressure from viscosity in incompressible Navier-Stokes dynamics, Seminaire du Laboratoire Jacques-Louis Lions, Universite Pierre et Marie Curie, France, June 17, 2005  
Divorcing pressure from viscosity in incompressible Navier-Stokes dynamics, Groupe de travail, Universite Paul Sabatier, France, June 16, 2005  
Divorcing pressure from viscosity in incompressible Navier-Stokes dynamics, International Conference on Multiscale Modeling and Scientific Computing, in honor of Professor Bjorn Engquist on occasion of his 60th birthday, Beijing, June, 2005  
Finite element Navier-Stokes solvers without Inf-Sup condition, International Conference on Scientific Computing, Nanjing, China,, June, 2005  
Divorcing pressure from viscosity in incompressible Navier-Stokes dynamics, The Nonlinear Partial Differential Equations: Analysis, Numerics and Applications, IMS/NUS, Singapore, May, 2005  
Divorcing pressure from viscosity in incompressible Navier-Stokes dynamics, Computational and Applied Mathematics Seminar, University of California, Irvine, April 22, 2005  
Divorcing pressure from viscosity in incompressible Navier-Stokes dynamics, Developments in Navier-Stokes Equations & Turbulence Research, IMS/NUS, Singapore, December, 2004  
Divorcing pressure from viscosity in incompressible Navier-Stokes dynamics, Third International Congress of Chinese Mathematicians, Hong Kong, December, 2004  
On incompressible Navier-Stokes dynamics: a new approach for analysis and computation, First Singapore Workshop on PDE and Scientific Computing, IMS/NUS, December, 2004  
Coarsening dynamics and continuum modeling for epitaxial growth of thin films, Nanoscale Material Interfaces: Experiment, Theory and Simulation, IMS/NUS, Singapore, November, 2004  
Energy and Helicity Preserving Schemes for Hydrodynamic, The Sixth International Workshop on Mathematical Aspects of Fluid , and Plasma Dynamics, Kyoto, Japan, September, 2004  
On incompressible Navier-Stokes dynamics: a new approach for analysis and computation, Plenary Lecturer, The Tenth International Conference on Hyperbolic Problems: Theory, Numerics and Applications, Osaka, Japan, September, 2004  
Divorcing pressure from viscosity in incompressible Navier-Stokes dynamics, Conference on Analysis, Modeling and Computation of PDE and Multiphase Flow, On the occasion of James Glimm's 70th Birthday, Stony Brook, August, 2004  
Numerical methods for simple and complex fluids, The third workshop on multiscale modeling of complex fluid", Peking University, July, 2004  
Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term, Int'l Workshop on Nonlinear Waves, On the occasion of George Papanicolaou's 60th Birthday, Hong Kong, June, 2004  
Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term, CSCAMM workshop on Analytical and Computational Challenges of Incompressible Flows at High Reynolds Number, Maryland, May, 2004  
Multi-Scale Phenomena in Complex Fluids: Modeling, Analysis and Simulation, Shanghai Summer School on Analysis and Numerics in Modern Sciences, Fudan University, May, 2004  
Fourth evolution PDE for image process, International Conference on Numerical Methods in Imaging Science and Information Processing, IMS/NUS, Singapore, December, 2003  
Concepts and application of time limiters to high resolution schemes, ICIAM'03, Mini-symposium on Kinetic Theory and Related Hyperbolic Problems, Sydney, Australia, July, 2003  
Ground state of nonlinear Schrodinger equation as a limit of a gradient flow, CSCAMM workshop on Analysis and Numerics for Modelling Semiconductor Devices and Biological Channels, Maryland, May, 2003  
A class of numerical methods based on local vorticity boundary conditions and local pressure boundary conditions, CSCAMM workshop on Perspectives on incompressible flows, comparison of different computational strategies, Maryland, April, 2003  
Efficient numerical methods for incompressible flows, Summer School of Mathematics for Graduate Students in China, Jinlin University, July, 2002  
Thin film epitaxy with the Ehrlich-Schwoebel effect, Workshop on Scientific Computing, Xiangtan University, China, July, 2002  
Thin film epitaxy with the Ehrlich-Schwoebel effect, IMS Workshop on PDE and Their Numerical Methods, Chinese University of Hong Kong, July, 2002  
Efficient numerical methods for incompressible flows, keynote Speaker, The Tenth South Eastern Approximation Theory Conference, Athens, Georgia, March, 2002  
Doctoral Theses Directed

Linbao Zhang, Multi-scale Modeling and Computations, (2009 PhD)  
Jie Liu, A Class of Efficient, Stable Navier-Stokes Solvers, (2006 PhD)  
kexue Liu, Nonlinear Evolutionary PDEs in Image Processing and Computer Vision, (2004 PhD)  
Jianjun Xu, Studies of High Order Finite/Spectral Element Methods for Unsteady Incompressible Viscous Flow, (2001 PhD)  
Cheng Wang, High Order Finite Difference Method for Incompressible Flow, (2000 PhD)  
Hans Johnston, Efficient Computation of Viscous Incompressible Flow, (1999 PhD)  
Hwajeong Choi, Robust Numerical Methods for Conservation Laws Using a Biased Averaging Procedure, (1997 PhD)  

Publications

Books

  1. Multi-scale phenomena in complex fluids, Modeling, Analysis and Numerical Simulations, edited by T. Hou, C. Liu and J.-G. Liu (2009), World Scientific, ISBN 978-981-4273-25-1
  2. Hyperbolic Problems: Theory, Numerics and Applications, volume I: Plenary & Invited Talks; volume II: Contributed Talks, Proceedings of Symposia in Applied Mathematics, edited by E. Tadmor, J.-G. Liu, and A.E. Tzavaras, vol. 67 (2009), American Mathematical Society, ISBN 978-0-8218-4728-2
  3. Dynamics in Models of Coarsening, Coagulation, Condensation and Quantization, edited by W. Bao and J.-G. Liu (2007), World Scientific, ISBN 9789812708502

Papers Published

  1. Degond, P; Frouvelle, A; Liu, JG, FROM KINETIC TO FLUID MODELS OF LIQUID CRYSTALS BY THE MOMENT METHOD, Kinetic and Related Models, vol. 15 no. 3 (June, 2022), pp. 417-465, American Institute of Mathematical Sciences (AIMS)
  2. Liu, JG; Wang, Z; Zhang, Y; Zhou, Z, RIGOROUS JUSTIFICATION OF THE FOKKER-PLANCK EQUATIONS OF NEURAL NETWORKS BASED ON AN ITERATION PERSPECTIVE, Siam Journal on Mathematical Analysis, vol. 54 no. 1 (January, 2022), pp. 1270-1312, Society for Industrial & Applied Mathematics (SIAM)
  3. Liu, JG; Zhang, Z, EXISTENCE of GLOBAL WEAK SOLUTIONS of p-NAVIER-STOKES EQUATIONS, Discrete and Continuous Dynamical Systems Series B, vol. 27 no. 1 (January, 2022), pp. 469-486, American Institute of Mathematical Sciences (AIMS)
  4. Gao, Y; Liu, JG, Surfactant-dependent contact line dynamics and droplet spreading on textured substrates: Derivations and computations, Physica D: Nonlinear Phenomena, vol. 428 (December, 2021)
  5. Gao, Y; Liu, JG; Liu, Z, Existence and rigidity of the vectorial peierls-nabarro model for dislocations in high dimensions, Nonlinearity, vol. 34 no. 11 (November, 2021), pp. 7778-7828
  6. Lafata, KJ; Chang, Y; Wang, C; Mowery, YM; Vergalasova, I; Niedzwiecki, D; Yoo, DS; Liu, J-G; Brizel, DM; Yin, F-F, Intrinsic radiomic expression patterns after 20 Gy demonstrate early metabolic response of oropharyngeal cancers., Med Phys, vol. 48 no. 7 (July, 2021), pp. 3767-3777
  7. Hu, J; Liu, JG; Xie, Y; Zhou, Z, A structure preserving numerical scheme for Fokker-Planck equations of neuron networks: Numerical analysis and exploration, Journal of Computational Physics, vol. 433 (May, 2021)
  8. Liu, JG; Wang, J; Zhao, Y; Zhou, Z, Field model for complex ionic fluids: Analytical properties and numerical investigation, Communications in Computational Physics, vol. 30 no. 3 (January, 2021), pp. 874-902
  9. Liu, JG; Xu, X, Existence and incompressible limit of a tissue growth model with autophagy, Siam Journal on Mathematical Analysis, vol. 53 no. 5 (January, 2021), pp. 5215-5242
  10. Li, Q; Liu, JG; Shu, R, Sensitivity analysis of burgers' equation with shocks, Siam/Asa Journal on Uncertainty Quantification, vol. 8 no. 4 (January, 2021), pp. 1493-1521, Society for Industrial & Applied Mathematics (SIAM)
  11. Gao, Y; Liu, JG, Gradient flow formulation and second order numerical method for motion by mean curvature and contact line dynamics on rough surface, Interfaces and Free Boundaries, vol. 23 no. 1 (January, 2021), pp. 103-158
  12. Gao, Y; Jin, G; Liu, J-G, Inbetweening auto-animation via Fokker-Planck dynamics and thresholding, Inverse Problems & Imaging, vol. 15 no. 5 (2021), pp. 843-843, American Institute of Mathematical Sciences (AIMS)
  13. Huang, H; Liu, JG; Pickl, P, On the Mean-Field Limit for the Vlasov–Poisson–Fokker–Planck System, Journal of Statistical Physics, vol. 181 no. 5 (December, 2020), pp. 1915-1965
  14. Gao, Y; Liu, JG; Lu, J; Marzuola, JL, Analysis of a continuum theory for broken bond crystal surface models with evaporation and deposition effects, Nonlinearity, vol. 33 no. 8 (August, 2020), pp. 3816-3845
  15. Jin, S; Li, L; Liu, JG, Convergence of the random batch method for interacting particles with disparate species and weights, Siam Journal on Numerical Analysis, vol. 59 no. 2 (March, 2020), pp. 746-768
  16. Jin, S; Li, L; Liu, JG, Random Batch Methods (RBM) for interacting particle systems, Journal of Computational Physics, vol. 400 (January, 2020)
  17. Feng, Y; Gao, T; Li, L; Liu, JG; Lu, Y, Uniform-in-time weak error analysis for stochastic gradient descent algorithms via diffusion approximation, Communications in Mathematical Sciences, vol. 18 no. 1 (January, 2020), pp. 163-188
  18. Degond, P; Engel, M; Liu, JG; Pego, RL, A markov jump process modelling animal group size statistics, Communications in Mathematical Sciences, vol. 18 no. 1 (January, 2020), pp. 55-89
  19. Li, L; Li, Y; Liu, JG; Liu, Z; Lu, J, A stochastic version of stein variational gradient descent for efficient sampling, Communications in Applied Mathematics and Computational Science, vol. 15 no. 1 (January, 2020), pp. 37-63, Mathematical Sciences Publishers
  20. Li, L; Liu, JG, Large time behaviors of upwind schemes and B-schemes for fokker-planck equations on R by jump processes, Mathematics of Computation, vol. 89 no. 325 (January, 2020), pp. 2283-2320, American Mathematical Society (AMS)
  21. Gao, Y; Liu, JG; Luo, T; Xiang, Y, Revisit of the peierls-nabarro model for edge dislocations in Hilbert space, Discrete and Continuous Dynamical Systems Series B, vol. 22 no. 11 (January, 2020)
  22. LIU, JG; WANG, J, GLOBAL EXISTENCE FOR NERNST-PLANCK-NAVIER-STOKES SYSTEM IN RN, Communications in Mathematical Sciences, vol. 18 no. 6 (January, 2020), pp. 1743-1754
  23. LIU, JIANGUO; XU, X, A CLASS OF FUNCTIONAL INEQUALITIES AND THEIR APPLICATIONS TO FOURTH-ORDER NONLINEAR PARABOLIC EQUATIONS, Communications in Mathematical Sciences, vol. 18 no. 7 (January, 2020), pp. 1911-1948, International Press of Boston
  24. Gao, Y; Liu, J-G, Long time behavior of dynamic solution to Peierls–Nabarro dislocation model, Methods and Applications of Analysis, vol. 27 no. 2 (2020), pp. 161-198, International Press of Boston
  25. Gao, Y; Liu, J-G, A note on parametric Bayesian inference via gradient flows, Annals of Mathematical Sciences and Applications, vol. 5 no. 2 (2020), pp. 261-282, International Press of Boston
  26. Li, L; Liu, JG; Yu, P, On the mean field limit for Brownian particles with Coulomb interaction in 3D, Journal of Mathematical Physics, vol. 60 no. 11 (November, 2019)
  27. Liu, JG; Pego, RL, On Local Singularities in Ideal Potential Flows with Free Surface, Chinese Annals of Mathematics, Series B, vol. 40 no. 6 (November, 2019), pp. 925-948
  28. Liu, JG; Pego, RL; Pu, Y, Well-posedness and derivative blow-up for a dispersionless regularized shallow water system, Nonlinearity, vol. 32 no. 11 (October, 2019), pp. 4346-4376
  29. Liu, JG; Pego, RL; Slepčev, D, Least action principles for incompressible flows and geodesics between shapes, Calculus of Variations and Partial Differential Equations, vol. 58 no. 5 (October, 2019)
  30. Lafata, KJ; Zhou, Z; Liu, J-G; Hong, J; Kelsey, CR; Yin, F-F, An Exploratory Radiomics Approach to Quantifying Pulmonary Function in CT Images., Scientific Reports, vol. 9 no. 1 (August, 2019), pp. 11509
  31. Liu, JG; Tang, M; Wang, L; Zhou, Z, Analysis and computation of some tumor growth models with nutrient: From cell density models to free boundary dynamics, Discrete and Continuous Dynamical Systems Series B, vol. 24 no. 7 (July, 2019), pp. 3011-3035
  32. Zhan, Q; Zhuang, M; Zhou, Z; Liu, JG; Liu, QH, Complete-Q Model for Poro-Viscoelastic Media in Subsurface Sensing: Large-Scale Simulation with an Adaptive DG Algorithm, Ieee Transactions on Geoscience and Remote Sensing, vol. 57 no. 7 (July, 2019), pp. 4591-4599, Institute of Electrical and Electronics Engineers (IEEE)
  33. Liu, JG; Niethammer, B; Pego, RL, Self-similar Spreading in a Merging-Splitting Model of Animal Group Size, Journal of Statistical Physics, vol. 175 no. 6 (June, 2019), pp. 1311-1330
  34. Liu, JG; Lu, J; Margetis, D; Marzuola, JL, Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model, Physica D: Nonlinear Phenomena, vol. 393 (June, 2019), pp. 54-67
  35. Gao, Y; Li, L; Liu, JG, Patched peakon weak solutions of the modified Camassa–Holm equation, Physica D: Nonlinear Phenomena, vol. 390 (March, 2019), pp. 15-35
  36. Zhan, Q; Zhuang, M; Fang, Y; Liu, J-G; Liu, QH, Green's function for anisotropic dispersive poroelastic media based on the Radon transform and eigenvector diagonalization., Proceedings. Mathematical, Physical, and Engineering Sciences, vol. 475 no. 2221 (January, 2019), pp. 20180610
  37. Lafata, KJ; Hong, JC; Geng, R; Ackerson, BG; Liu, J-G; Zhou, Z; Torok, J; Kelsey, CR; Yin, F-F, Association of pre-treatment radiomic features with lung cancer recurrence following stereotactic body radiation therapy., Phys Med Biol, vol. 64 no. 2 (January, 2019), pp. 025007
  38. Huang, H; Liu, JG; Lu, J, Learning interacting particle systems: Diffusion parameter estimation for aggregation equations, Mathematical Models and Methods in Applied Sciences, vol. 29 no. 1 (January, 2019), pp. 1-29
  39. Frouvelle, A; Liu, JG, Long-Time Dynamics for a Simple Aggregation Equation on the Sphere, Springer Proceedings in Mathematics and Statistics, vol. 282 (January, 2019), pp. 457-479, ISBN 9783030150952
  40. Gao, Y; Liu, JG; Lu, XY, Gradient flow approach to an exponential thin film equation: Global existence and latent singularity, Esaim: Control, Optimisation and Calculus of Variations, vol. 25 (January, 2019), pp. 49-49, E D P SCIENCES
  41. De Hoop, MV; Liu, JG; Markowich, PA; Ussembayev, NS, Plane-wave analysis of a hyperbolic system of equations with relaxation in ℝd, Communications in Mathematical Sciences, vol. 17 no. 1 (January, 2019), pp. 61-79
  42. Liu, A; Liu, JG; Lu, Y, On the rate of convergence of empirical measure in ∞-Wasserstein distance for unbounded density function, Quarterly of Applied Mathematics, vol. 77 no. 4 (January, 2019), pp. 811-829
  43. Li, L; Liu, JG, A discretization of Caputo derivatives with application to time fractional SDEs and gradient flows, Siam Journal on Numerical Analysis, vol. 57 no. 5 (January, 2019), pp. 2095-2120
  44. Liu, JG; Strain, RM, Global stability for solutions to the exponential PDE describing epitaxial growth, Interfaces and Free Boundaries, vol. 21 no. 1 (January, 2019), pp. 61-86
  45. Lafata, K; Zhou, Z; Liu, JG; Yin, FF, Data clustering based on Langevin annealing with a self-consistent potential, Quarterly of Applied Mathematics, vol. 77 no. 3 (January, 2019), pp. 591-613
  46. Hu, W; Li, CJ; Li, L; Liu, J-G, On the diffusion approximation of nonconvex stochastic gradient descent, Annals of Mathematical Sciences and Applications, vol. 4 no. 1 (2019), pp. 3-32, International Press of Boston
  47. Gao, Y; Ji, H; Liu, JG; Witelski, TP, A vicinal surface model for epitaxial growth with logarithmic free energy, Discrete and Continuous Dynamical Systems Series B, vol. 23 no. 10 (December, 2018), pp. 4433-4453, American Institute of Mathematical Sciences (AIMS)
  48. Feng, Y; Li, L; Liu, JG; Xu, X, Continuous and discrete one dimensional autonomous fractional odes, Discrete and Continuous Dynamical Systems Series B, vol. 23 no. 8 (October, 2018), pp. 3109-3135, American Institute of Mathematical Sciences (AIMS)
  49. Feng, Y; Li, L; Liu, JG; Xu, X, A note on one-dimensional time fractional ODEs, Applied Mathematics Letters, vol. 83 (September, 2018), pp. 87-94, Elsevier BV
  50. Li, L; Liu, JG; Wang, L, Cauchy problems for Keller–Segel type time–space fractional diffusion equation, Journal of Differential Equations, vol. 265 no. 3 (August, 2018), pp. 1044-1096, Elsevier BV
  51. Gao, Y; Liu, JG, The modified camassa-holm equation in lagrangian coordinates, Discrete and Continuous Dynamical Systems Series B, vol. 23 no. 6 (August, 2018), pp. 2545-2592, American Institute of Mathematical Sciences (AIMS)
  52. Liu, JG; Tang, M; Wang, L; Zhou, Z, An accurate front capturing scheme for tumor growth models with a free boundary limit, Journal of Computational Physics, vol. 364 (July, 2018), pp. 73-94, Elsevier BV
  53. Chen, K; Li, Q; Liu, JG, Online learning in optical tomography: A stochastic approach, Inverse Problems, vol. 34 no. 7 (May, 2018), pp. 075010-075010, IOP Publishing
  54. Liu, JG; Xu, X, Partial regularity of weak solutions to a PDE system with cubic nonlinearity, Journal of Differential Equations, vol. 264 no. 8 (April, 2018), pp. 5489-5526, ACADEMIC PRESS INC ELSEVIER SCIENCE
  55. Li, L; Liu, JG, p-Euler equations and p-Navier–Stokes equations, Journal of Differential Equations, vol. 264 no. 7 (April, 2018), pp. 4707-4748, Elsevier BV
  56. Gao, Y; Liu, JG; Lu, XY; Xu, X, Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface, Calculus of Variations and Partial Differential Equations, vol. 57 no. 2 (April, 2018), Springer Nature
  57. Feng, Y; Li, L; Liu, JG, Semigroups of stochastic gradient descent and online principal component analysis: Properties and diffusion approximations, Communications in Mathematical Sciences, vol. 16 no. 3 (January, 2018), pp. 777-789
  58. Li, L; Liu, JG, Some compactness criteria for weak solutions of time fractional pdes, Siam Journal on Mathematical Analysis, vol. 50 no. 4 (January, 2018), pp. 3963-3995, Society for Industrial & Applied Mathematics (SIAM)
  59. Gao, Y; Li, L; Liu, JG, A dispersive regularization for the modified camassa–holm equation, Siam Journal on Mathematical Analysis, vol. 50 no. 3 (January, 2018), pp. 2807-2838, Society for Industrial & Applied Mathematics (SIAM)
  60. Li, L; Liu, JG, A generalized definition of caputo derivatives and its application to fractional odes, Siam Journal on Mathematical Analysis, vol. 50 no. 3 (January, 2018), pp. 2867-2900, Society for Industrial & Applied Mathematics (SIAM)
  61. Li, L; Liu, JG, A note on deconvolution with completely monotone sequences and discrete fractional calculus, Quarterly of Applied Mathematics, vol. 76 no. 1 (January, 2018), pp. 189-198, American Mathematical Society (AMS)
  62. Coquel, F; Jin, S; Liu, JG; Wang, L, Entropic sub-cell shock capturing schemes via Jin-Xin relaxation and glimm front sampling for scalar conservation laws, Mathematics of Computation, vol. 87 no. 311 (January, 2018), pp. 1083-1126, American Mathematical Society (AMS)
  63. Liu, JG; Wang, L; Zhou, Z, Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations, Mathematics of Computation, vol. 87 no. 311 (January, 2018), pp. 1165-1189, American Mathematical Society (AMS)
  64. Jin, S; Liu, J-G; Ma, Z, Uniform spectral convergence of the stochastic Galerkin method for the linear transport equations with random inputs in diffusive regime and a micro–macro decomposition-based asymptotic-preserving method, Research in the Mathematical Sciences, vol. 4 no. 1 (December, 2017), Springer Science and Business Media LLC
  65. Li, L; Liu, JG; Lu, J, Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem, Journal of Statistical Physics, vol. 169 no. 2 (October, 2017), pp. 316-339, Springer Nature America, Inc
  66. Liu, JG; Ma, Z; Zhou, Z, Explicit and Implicit TVD Schemes for Conservation Laws with Caputo Derivatives, Journal of Scientific Computing, vol. 72 no. 1 (July, 2017), pp. 291-313, Springer Nature
  67. Gao, Y; Ji, H; Liu, JG; Witelski, TP, Global existence of solutions to a tear film model with locally elevated evaporation rates, Physica D: Nonlinear Phenomena, vol. 350 (July, 2017), pp. 13-25, Elsevier BV
  68. Gao, Y; Liu, JG; Lu, J, Continuum Limit of a Mesoscopic Model with Elasticity of Step Motion on Vicinal Surfaces, Journal of Nonlinear Science, vol. 27 no. 3 (June, 2017), pp. 873-926, Springer Nature
  69. Liu, JG; Wang, J, Global existence for a thin film equation with subcritical mass, Discrete and Continuous Dynamical Systems Series B, vol. 22 no. 4 (June, 2017), pp. 1461-1492, American Institute of Mathematical Sciences (AIMS)
  70. Degond, P; Liu, JG; Pego, RL, Coagulation–Fragmentation Model for Animal Group-Size Statistics, Journal of Nonlinear Science, vol. 27 no. 2 (April, 2017), pp. 379-424, Springer Nature
  71. Cong, W; Liu, JG, Uniform L∞ boundedness for a degenerate parabolic-parabolic Keller-Segel model, Discrete and Continuous Dynamical Systems Series B, vol. 22 no. 2 (March, 2017), pp. 307-338, American Institute of Mathematical Sciences (AIMS)
  72. Gao, Y; Liu, JG; Lu, J, Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime, Siam Journal on Mathematical Analysis, vol. 49 no. 3 (January, 2017), pp. 1705-1731, Society for Industrial & Applied Mathematics (SIAM)
  73. Liu, JG; Wang, J, A generalized Sz. Nagy inequality in higher dimensions and the critical thin film equation, Nonlinearity, vol. 30 no. 1 (January, 2017), pp. 35-60, IOP Publishing
  74. Huang, H; Liu, JG, Discrete-in-time random particle blob method for the Keller-Segel equation and convergence analysis, Communications in Mathematical Sciences, vol. 15 no. 7 (January, 2017), pp. 1821-1842, International Press of Boston
  75. Degond, P; Herty, M; Liu, JG, Meanfield games and model predictive control, Communications in Mathematical Sciences, vol. 15 no. 5 (January, 2017), pp. 1403-1422, International Press of Boston
  76. Degond, P; Liu, JG; Merino-Aceituno, S; Tardiveau, T, Continuum dynamics of the intention field under weakly cohesive social interaction, Mathematical Models and Methods in Applied Sciences, vol. 27 no. 1 (January, 2017), pp. 159-182, World Scientific Pub Co Pte Lt
  77. Liu, JG; Yang, R, A random particle blob method for the keller-segel equation and convergence analysis, Mathematics of Computation, vol. 86 no. 304 (January, 2017), pp. 725-745, American Mathematical Society (AMS)
  78. Gao, Y; Liu, JG, Global convergence of a sticky particle method for the modified Camassa-Holm equation, Siam Journal on Mathematical Analysis, vol. 49 no. 2 (January, 2017), pp. 1267-1294, Society for Industrial & Applied Mathematics (SIAM)
  79. Liu, JG; Xu, X, Analytical validation of a continuum model for the evolution of a crystal surface in multiple space dimensions, Siam Journal on Mathematical Analysis, vol. 49 no. 3 (January, 2017), pp. 2220-2245, Society for Industrial & Applied Mathematics (SIAM)
  80. Huang, H; Liu, JG, Error estimate of a random particle blob method for the Keller-Segel equation, Mathematics of Computation, vol. 86 no. 308 (January, 2017), pp. 2719-2744, American Mathematical Society (AMS)
  81. Huang, H; Liu, JG, Error estimates of the aggregation-diffusion splitting algorithms for the Keller-Segel equations, Discrete and Continuous Dynamical Systems Series B, vol. 21 no. 10 (December, 2016), pp. 3463-3478, American Institute of Mathematical Sciences (AIMS)
  82. Liu, J-G; Yang, R, Propagation of chaos for large Brownian particle system with Coulomb interaction, Research in the Mathematical Sciences, vol. 3 no. 1 (December, 2016), Springer Science and Business Media LLC
  83. Huang, H; Liu, JG, A note on Monge-Ampère Keller-Segel equation, Applied Mathematics Letters, vol. 61 (November, 2016), pp. 26-34, Elsevier BV
  84. Liu, JG; Wang, J, A Note on L∞-Bound and Uniqueness to a Degenerate Keller-Segel Model, Acta Applicandae Mathematicae, vol. 142 no. 1 (April, 2016), pp. 173-188, Springer Nature, ISSN 0167-8019
  85. Herschlag, G; Liu, JG; Layton, AT, Fluid extraction across pumping and permeable walls in the viscous limit, Physics of Fluids, vol. 28 no. 4 (April, 2016), pp. 041902-041902, AIP Publishing, ISSN 1070-6631
  86. Liu, J-G; Wang, J, Refined hyper-contractivity and uniqueness for the Keller–Segel equations, Applied Mathematics Letters, vol. 52 (February, 2016), pp. 212-219, Elsevier BV
  87. Chen, J; Liu, JG; Zhou, Z, On a Schrödinger-Landau-Lifshitz system: Variational structure and numerical methods, Multiscale Modeling & Simulation, vol. 14 no. 4 (January, 2016), pp. 1463-1487, Society for Industrial & Applied Mathematics (SIAM)
  88. Huang, H; Liu, JG, Well-posedness for the keller-segel equation with fractional laplacian and the theory of propagation of chaos, Kinetic and Related Models, vol. 9 no. 4 (January, 2016), pp. 715-748
  89. Cong, W; Liu, JG, A degenerate p-laplacian keller-segel model, Kinetic and Related Models, vol. 9 no. 4 (January, 2016), pp. 687-714, American Institute of Mathematical Sciences (AIMS)
  90. Liu, JG; Xu, X, Existence theorems for a multidimensional crystal surface model, Siam Journal on Mathematical Analysis, vol. 48 no. 6 (January, 2016), pp. 3667-3687, Society for Industrial & Applied Mathematics (SIAM)
  91. Liu, JG; Pego, RL, On generating functions of hausdorff moment sequences, Transactions of the American Mathematical Society, vol. 368 no. 12 (January, 2016), pp. 8499-8518, American Mathematical Society (AMS)
  92. Liu, JG; Zhang, Y, Convergence of diffusion-drift many particle systems in probability under a sobolev norm, Proceedings of Particle Systems and Partial Differential Equations - III, Springer Proceedings in Mathematics and Statistics, vol. 162 (January, 2016), pp. 195-223, Springer International Publishing, ISBN 9783319321424
  93. Duan, Y; Liu, J-G, Error estimate of the particle method for the $b$-equation, Methods and Applications of Analysis, vol. 23 no. 2 (2016), pp. 119-154, International Press of Boston
  94. Liu, J-G; Zhang, Y, Convergence of stochastic interacting particle systems in probability under a Sobolev norm, Annals of Mathematical Sciences and Applications, vol. 1 no. 2 (2016), pp. 251-299, International Press of Boston
  95. Degond, P; Frouvelle, A; Liu, JG, Phase Transitions, Hysteresis, and Hyperbolicity for Self-Organized Alignment Dynamics, Archive for Rational Mechanics and Analysis, vol. 216 no. 1 (April, 2015), pp. 63-115
  96. Xue, Y; Wang, C; Liu, JG, Simple Finite Element Numerical Simulation of Incompressible Flow Over Non-rectangular Domains and the Super-Convergence Analysis, Journal of Scientific Computing, vol. 65 no. 3 (March, 2015), pp. 1189-1216, Springer Nature, ISSN 0885-7474
  97. Lu, J; Liu, JG; Margetis, D, Emergence of step flow from an atomistic scheme of epitaxial growth in 1+1 dimensions, Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, vol. 91 no. 3 (March, 2015), pp. 032403, ISSN 1539-3755
  98. Chertock, A; Liu, JG; Pendleton, T, Elastic collisions among peakon solutions for the Camassa-Holm equation, Applied Numerical Mathematics, vol. 93 (January, 2015), pp. 30-46, Elsevier BV, ISSN 0168-9274
  99. Herschlag, G; Liu, JG; Layton, AT, An exact solution for stokes flow in a channel with arbitrarily large wall permeability, Siam Journal on Applied Mathematics, vol. 75 no. 5 (January, 2015), pp. 2246-2267, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1399
  100. Degond, P; Liu, J-G; Ringhofer, C, Evolution of wealth in a non-conservative economy driven by local Nash equilibria., Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences, vol. 372 no. 2028 (November, 2014), pp. 20130394-20130394, The Royal Society, ISSN 1364-503X
  101. Coquel, F; Jin, S; Liu, JG; Wang, L, Well-Posedness and Singular Limit of a Semilinear Hyperbolic Relaxation System with a Two-Scale Discontinuous Relaxation Rate, Archive for Rational Mechanics and Analysis, vol. 214 no. 3 (October, 2014), pp. 1051-1084, ISSN 0003-9527
  102. Johnston, H; Wang, C; Liu, JG, A Local Pressure Boundary Condition Spectral Collocation Scheme for the Three-Dimensional Navier–Stokes Equations, Journal of Scientific Computing, vol. 60 no. 3 (September, 2014), pp. 612-626, Springer Nature, ISSN 0885-7474
  103. Duan, Y; Liu, JG, Convergence analysis of the vortex blob method for the b-equation, Discrete and Continuous Dynamical Systems Series A, vol. 34 no. 5 (May, 2014), pp. 1995-2011, American Institute of Mathematical Sciences (AIMS), ISSN 1078-0947
  104. Bian, S; Liu, JG; Zou, C, Ultra-contractivity for keller-segel model with diffusion exponent m > 1-2/d, Kinetic and Related Models, vol. 7 no. 1 (March, 2014), pp. 9-28, American Institute of Mathematical Sciences (AIMS), ISSN 1937-5093
  105. Degond, P; Herty, M; Liu, JG, Flow on sweeping networks, Multiscale Modeling & Simulation, vol. 12 no. 2 (January, 2014), pp. 538-565, Society for Industrial & Applied Mathematics (SIAM), ISSN 1540-3459
  106. Chen, X; Li, X; Liu, JG, Existence and uniqueness of global weak solution to a kinetic model for the sedimentation of rod-like particles, Communications in Mathematical Sciences, vol. 12 no. 8 (January, 2014), pp. 1579-1601, International Press of Boston, ISSN 1539-6746
  107. Degond, P; Frouvelle, A; Liu, J-G, A NOTE ON PHASE TRANSITIONS FOR THE SMOLUCHOWSKI EQUATION WITH DIPOLAR POTENTIAL, in Proceedings of the Fourteenth International Conference on Hyperbolic Problems: Theory, Numerics and Application, edited by Ancona, F; Bressan, A; Marcati, P; Marson, A, Hyperbolic Problems: Theory, Numerics, Applications, vol. 8 (January, 2014), pp. 179-192, AMER INST MATHEMATICAL SCIENCES-AIMS
  108. Chae, D; Degond, P; Liu, JG, Well-posedness for hall-magnetohydrodynamics, Annales De L'Institut Henri Poincare (C) Non Linear Analysis, vol. 31 no. 3 (January, 2014), pp. 555-565
  109. Goudon, T; Jin, S; Liu, J-G; Yan, B, Asymptotic-preserving schemes for kinetic-fluid modeling of disperse two-phase flows with variable fluid density, International Journal for Numerical Methods in Fluids, vol. 75 no. 2 (2014), pp. 81-102, WILEY, ISSN 0271-2091
  110. Huang, YL; Liu, JG; Wang, WC, A generalized mac scheme on curvilinear domains, Siam Journal on Scientific Computing, vol. 35 no. 5 (November, 2013), pp. B953-B986, Society for Industrial & Applied Mathematics (SIAM), ISSN 1064-8275
  111. Bian, S; Liu, JG, Dynamic and Steady States for Multi-Dimensional Keller-Segel Model with Diffusion Exponent m > 0, Communications in Mathematical Physics, vol. 323 no. 3 (November, 2013), pp. 1017-1070, Springer Nature, ISSN 0010-3616
  112. Chen, X; Liu, JG, Analysis of polymeric flow models and related compactness theorems in weighted spaces, Siam Journal on Mathematical Analysis, vol. 45 no. 3 (October, 2013), pp. 1179-1215, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1410
  113. Goudon, T; Jin, S; Liu, JG; Yan, B, Asymptotic-preserving schemes for kinetic-fluid modeling of disperse two-phase flows, Journal of Computational Physics, vol. 246 (August, 2013), pp. 145-164, Elsevier BV, ISSN 0021-9991
  114. Chen, X; Liu, JG, Global weak entropy solution to Doi-Saintillan-Shelley model for active and passive rod-like and ellipsoidal particle suspensions, Journal of Differential Equations, vol. 254 no. 7 (April, 2013), pp. 2764-2802, Elsevier BV, ISSN 0022-0396
  115. P. Degond, A. Frouvelle, J.-G. Liu, S Motsch, L Navoret, Macroscopic models of collective motion and self-organization, Seminaire Laurent Schwartz -- EDP et applicatios, vol. 2012 - 2013 (2013), pp. 1-27
  116. Degond, P; Liu, J-G; Ringhofer, C, Evolution of the Distribution of Wealth in an Economic Environment Driven by Local Nash Equilibria, Journal of Statistical Physics, vol. 154 no. 3 (2013), pp. 1-30, Springer Nature, ISSN 0022-4715
  117. Chen, X; Jüngel, A; Liu, J-G, A Note on Aubin-Lions-Dubinskiǐ Lemmas, Acta Applicandae Mathematicae, vol. 133 no. 1 (2013), pp. 1-11, ISSN 0167-8019
  118. Degond, P; Liu, J-G; Ringhofer, C, Large-Scale Dynamics of Mean-Field Games Driven by Local Nash Equilibria, Journal of Nonlinear Science, vol. 24 no. 1 (2013), pp. 1-23, ISSN 0938-8974
  119. Chae, D; Degond, P; Liu, J-G, Well-posedness for Hall-magnetohydrodynamics, Annales De L'Institut Henri Poincare (C) Non Linear Analysis, vol. 31 no. 3 (2013), pp. 555-565, Elsevier BV, ISSN 0294-1449
  120. Jin, S; Liu, JG; Wang, L, A domain decomposition method for semilinear hyperbolic systems with two-scale relaxations, Math. Comp., vol. 82 no. 282 (2013), pp. 749-779, American Mathematical Society (AMS)
  121. Degond, P; Liu, J-G; Motsch, S; Panferov, V, Hydrodynamic models of self-organized dynamics: Derivation and existence theory, Methods and Applications of Analysis, vol. 20 no. 2 (2013), pp. 89-114, International Press of Boston
  122. A. Chertock, J.-G. Liu, and T. Pendleton, Convergence analysis of the particle method for the Camassa-Holm equation, in Proceedings of the 13th International Conference on ``Hyperbolic Problems: Theory, Numerics and Applications" (2012), pp. 365-373, Higher Education Press, Beijing
  123. Chae, D; Liu, JG, Blow-up, zero alpha limit and the Liouville type theorem for the Euler-Poincare equations, Comm. Math. Phy.,, vol. 314 no. 3 (2012), pp. 671-687, Springer Nature, ISSN 0010-3616
  124. Chen, X; Liu, JG, Two Nonlinear Compactness Theorems in L^p(0,T;B), Appl. Math. Lett., vol. 25 no. 12 (2012), pp. 2252-2257, Elsevier BV, ISSN 0893-9659
  125. Chen, L; Liu, JG; Wang, J, Multi-dimensional degenerate Keller-Segel system with critical diffusion exponent 2n/(n+2), Siam J. Math Anal, vol. 44 no. 2 (2012), pp. 1077-1102, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1410
  126. Frouvelle, A; Liu, JG, Dynamics in a kinetic model of oriented particles with phase transition, Siam J. Math Anal, vol. 44 no. 2 (2012), pp. 791-826, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1410
  127. Carrillo, J; Chen, L; Liu, JG; Wang, J, A note on the subcritical two dimensional Keller-Segel system, Acta Applicanda Mathematicae, vol. 119 no. 1 (2012), pp. 43-55, Springer Nature, ISSN 0167-8019
  128. Degond, P; Liu, JG, Hydrodynamics of self-alignment interactions with precession and derivation of the Landau-Lifschitz-Gilbert equation, Math. Models Methods Appl. Sci., vol. 22 no. SUPPL.1 (2012), pp. 1114001-1114018, World Scientific Pub Co Pte Lt, ISSN 0218-2025
  129. Chertock, A; Liu, JG; Pendleton, T, Convergence of a particle method and global weak solutions of a family of evolutionary PDEs, Siam J. Numer. Anal., vol. 50 no. 1 (2012), pp. 1-21, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1429
  130. Haack, J; Jin, S; Liu, JG, An all-speed asymptotic-preserving method for the isentropic Euler and Navier-Stokes equations, Commun. Comput. Phy., vol. 12 no. 4 (2012), pp. 955-980, Global Science Press, ISSN 1815-2406
  131. Degond, P; Frouvell, A; Liu, JG, Macroscopic limits and phase transition in a system of self-propelled particles, J Nonlinear Sci., vol. 23 no. 3 (2012), pp. 427-456, Springer Nature, ISSN 0938-8974
  132. Zheng, W; Gao, H; Liu, JG; Zhang, Y; Ye, Q; Swank, C, General solution to gradient-induced transverse and longitudinal relaxation of spins undergoing restricted diffusion, Physical Review A, vol. 84 no. 5 (November, 2011), pp. 053411-8, American Physical Society (APS), ISSN 1050-2947
  133. Liu, JG; Lorz, A, A coupled chemotaxis-fluid model: Global existence, Ann. I. H. Poincare, An, vol. 28 no. 5 (2011), pp. 643-652, Elsevier BV, ISSN 0294-1449
  134. Acheritogaray, M; Degond, P; Frouvelle, A; Liu, JG, Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system, Kinetic and Related Models, vol. 4 no. 4 (2011), pp. 901-918, American Institute of Mathematical Sciences (AIMS), ISSN 1937-5093
  135. Huang, YL; Liu, JG; Wang, WC, An FFT based fast Poisson solver on spherical shells, Commun. Comput. Phy., vol. 9 no. 3 (2011), pp. 649-667, Global Science Press, ISSN 1815-2406
  136. Liu, JG; Liu, J; Pego, RL, Stable and accurate pressure approximation for unsteady incompressible viscous flow, Journal of Computational Physics, vol. 229 no. 9 (January, 2010), pp. 3428-3453, Elsevier BV, ISSN 0021-9991
  137. Liu, JG; Pego, RL, Stable discretization of magnetohydrodynamics in bounded domains, Communications in Mathematical Sciences, vol. 8 no. 1 (January, 2010), pp. 235-251, International Press of Boston, ISSN 1539-6746
  138. Liu, JG; Mieussens, L, Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit, Siam J. Numer. Anal., vol. 48 no. 4 (2010), pp. 1474-1491, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1429
  139. Liu, JG; Pego, R, Stable discretization of magnetohydrodynamics in bounded domains, Commun. Math. Sci., vol. 8 no. 1 (2010), pp. 234-251, INT PRESS BOSTON, INC, ISSN 1539-6746
  140. Liu, JG; Liu, J; Pego, RL, Error estimates for finite-element Navier-Stokes solvers without standard Inf-Sup conditions, Chinese Annals of Mathematics, Series B, vol. 30 no. 6 (December, 2009), pp. 743-768, Springer Nature, ISSN 0252-9599
  141. Liu, JG; Wang, WC, Characterization and regularity for axisymmetric solenoidal vector elds with application to Navier-Stokes equation, Siam J. Math. Anal., vol. 41 no. 5 (2009), pp. 1825-1850, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1410
  142. Ha, SY; Liu, JG, A simple proof of the Cucker-Smale flocking dynamics and mean-field limit, Commun. Math. Sci., vol. 7 no. 2 (2009), pp. 297-325, International Press of Boston, ISSN 1539-6746
  143. Degond, P; Liu, JG; Vignal, MH, Analysis of an asymptotic preserving scheme for the Euler-Poisson system in the quasineutral limit, Siam Journal on Numerical Analysis, vol. 46 no. 3 (November, 2008), pp. 1298-1322, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1429
  144. Lin, P; Liu, JG; Lu, X, Long time numerical solution of the Navier-Stokes equations based on a sequential regularization formulation, Siam Journal on Scientific Computing, vol. 31 no. 1 (November, 2008), pp. 398-419, Society for Industrial & Applied Mathematics (SIAM), ISSN 1064-8275
  145. Lu, X; Lin, P; Liu, JG, Analysis of a sequential regularization method for the unsteady Navier-Stokes equations, Mathematics of Computation, vol. 77 no. 263 (July, 2008), pp. 1467-1494, American Mathematical Society (AMS), ISSN 0025-5718
  146. Liu, JG; Wang, C, A fourth order numerical method for the primtive equations formulated in mean vorticity, Communications in Computational Physics, vol. 4 no. 1 (January, 2008), pp. 26-55, ISSN 1815-2406
  147. Hsia, CH; Liu, JG; Wang, C, Structural stability and bifurcation for 2D incompressible ows with symmetry, Meth. Appl. Anal., vol. 15 (2008), pp. 495-512
  148. Antman, SS; Liu, JG, Basic themes and pretty problems of nonlinear solid mechanics, Milan Journal of Mathematics, vol. 75 no. 1 (December, 2007), pp. 135-176, Springer Nature, ISSN 1424-9286
  149. Moore, J; Cheng, Z; Hao, J; Guo, G; Liu, J-G; Lin, C; Yu, LL, Effects of solid-state yeast treatment on the antioxidant properties and protein and fiber compositions of common hard wheat bran., Journal of Agricultural and Food Chemistry, vol. 55 no. 25 (December, 2007), pp. 10173-10182, ISSN 0021-8561 (published on Web 10/30/2007.)
  150. Liu, JG; Liu, J; Pego, RL, Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate, Communications on Pure and Applied Mathematics, vol. 60 no. 10 (October, 2007), pp. 1443-1487, WILEY, ISSN 0010-3640
  151. J.-G. Liu, Jie Liu and R. Pego, Estimates on the Stokes pressure by partitioning the energy of harmonic functions, in Kyoto Conference on the Navier-Stokes equations and their Applications, edited by Y. Giga, H. Kozono, H. Okamoto and Y. Shibta (2007), pp. 251--270, Kyoto Univ.
  152. Liu, JG; Liu, J; Pego, R, Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate via a commutator estimate, Comm. Pure Appl. Math., vol. 60 (2007), pp. 1443-1487
  153. Degond, P; Jin, S; Liu, JG, Mach-number uniform asymptotic- preserving Gauge schemes for compressible flows, Bulletin of the Institute of Mathematics Academia Sinica (New Series), vol. 2 (2007), pp. 851-892
  154. Liu, JG; Wang, WC, Convergence analysis of the energy and helicity preserving scheme for axisymmetric flows, Siam Journal on Numerical Analysis, vol. 44 no. 6 (December, 2006), pp. 2456-2480, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1429
  155. Degond, P; Liu, JG; Mieussens, L, Macroscopic fluid models with localized kinetic upscaling effects, Multiscale Modeling & Simulation, vol. 5 no. 3 (September, 2006), pp. 940-979, Society for Industrial & Applied Mathematics (SIAM), ISSN 1540-3459
  156. Moore, J; Liu, J-G; Zhou, K; Yu, LL, Effects of genotype and environment on the antioxidant properties of hard winter wheat bran., Journal of Agricultural and Food Chemistry, vol. 54 no. 15 (July, 2006), pp. 5313-5322, ISSN 0021-8561
  157. J.-G. Liu, Jie Liu and R. Pego, On incompressible Navier-Stokes dynamics: a new approach for analysis and computation, in Proceedings of the Tenth International Conference on Hyperbolic Problems, edited by F. Asakura, etc (2006), pp. 29--44, Yokohama Publishers, Inc.
  158. Liu, JG; Samelson, R; Wang, C, Global weak solution of planetary geostrophic equations with inviscid geostrophic balance, Applicable Analysis, vol. 85 no. 6-7 (2006), pp. 593-605
  159. Liu, JG; Wang, WC, Energy and helicity preserving schemes for hydro- and magnetohydro-dynamics flows with symmetry, Journal of Computational Physics, vol. 200 no. 1 (October, 2004), pp. 8-33, Elsevier BV
  160. Ghil, M; Liu, JG; Wang, C; Wang, S, Boundary-layer separation and adverse pressure gradient for 2-D viscous incompressible flow, Physica D: Nonlinear Phenomena, vol. 197 no. 1-2 (October, 2004), pp. 149-173, Elsevier BV, ISSN 0167-2789
  161. Li, B; Liu, JG, Epitaxial growth without slope selection: Energetics, coarsening, and dynamic scaling, Journal of Nonlinear Science, vol. 14 no. 5 (October, 2004), pp. 429-451, Springer Nature, ISSN 0938-8974
  162. Johnston, H; Liu, JG, Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term, Journal of Computational Physics, vol. 199 no. 1 (September, 2004), pp. 221-259, Elsevier BV
  163. Wang, C; Liu, JG; Johnston, H, Analysis of a fourth order finite difference method for the incompressible Boussinesq equations, Numerische Mathematik, vol. 97 no. 3 (May, 2004), pp. 555-594, Springer Nature
  164. Lin, HE; Liu, JG; Xu, WQ, Effects of small viscosity and far field boundary conditions for hyperbolic systems, Communications on Pure and Applied Analysis, vol. 3 no. 2 (January, 2004), pp. 267-290, American Institute of Mathematical Sciences (AIMS), ISSN 1534-0392
  165. Liu, JG; Xu, WQ, Far field boundary condition for convection diffusion equation at zero viscosity limit, Quarterly of Applied Mathematics, vol. 62 no. 1 (January, 2004), pp. 27-52, American Mathematical Society (AMS)
  166. Liu, JG; Wang, C, High order finite difference methods for unsteady incompressible flows in multi-connected domains, Computers & Fluids, vol. 33 no. 2 (January, 2004), pp. 223-255, Elsevier BV
  167. Li, B; Liu, JG, Eptaxial growth without slope selection: energetics, coarsening, and dynamic scaling, J. Nonlinear Sci., vol. 14 no. 5 (2004), pp. 429-451, ISSN 0938-8974
  168. Liu, JG; Wang, C, High order finite difference method for unsteady incompressible flow on multi-connected domain in vorticity-stream function formulation, Computer and Fluids, vol. 33 no. 2 (2004), pp. 223-255
  169. Duraisamy, K; Baeder, JD; Liu, JG, Concepts and Application of Time-Limiters to High Resolution Schemes, Journal of Scientific Computing, vol. 19 no. 1-3 (December, 2003), pp. 139-162, ISSN 0885-7474
  170. Li, B; Liu, JG, Thin film epitaxy with or without slope selection, European Journal of Applied Mathematics, vol. 14 no. 6 (December, 2003), pp. 713-743, Cambridge University Press (CUP)
  171. Liu, JG; Wang, C; Johnston, H, A Fourth Order Scheme for Incompressible Boussinesq Equations, Journal of Scientific Computing, vol. 18 no. 2 (April, 2003), pp. 253-285, ISSN 0885-7474
  172. Wang, C; Liu, JG, Positivity property of second-order flux-splitting schemes for the compressible Euler equations, Discrete and Continuous Dynamical Systems Series B, vol. 3 no. 2 (January, 2003), pp. 201-228, American Institute of Mathematical Sciences (AIMS)
  173. Chainais-Hillairet, C; Liu, JG; Peng, YJ, Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis, Esaim: Mathematical Modelling and Numerical Analysis, vol. 37 no. 2 (January, 2003), pp. 319-338, E D P SCIENCES
  174. Wang, C; Liu, JG, Fourth order convergence of a compact difference solver for incompressible flow, Commun. Appl. Anal., vol. 7 (2003), pp. 171-191
  175. Weinan, E; Liu, JG, Gauge method for viscous incompressible flows, Comm. Math. Sci., vol. 1 (2003), pp. 317-332
  176. Chern, IL; Liu, JG; Wang, WC, Accurate evaluation of electrostatics for macromolecules in solution, Methods and Applications of Analysis, vol. 10 (2003), pp. 309-328
  177. Johnston, H; Liu, JG, Finite difference schemes for incompressible flow based on local pressure boundary conditions, Journal of Computational Physics, vol. 180 no. 1 (July, 2002), pp. 120-154, Elsevier BV, ISSN 0021-9991
  178. Wang, C; Liu, JG, Analysis of finite difference schemes for unsteady Navier-Stokes equations in vorticity formulation, Numerische Mathematik, vol. 91 no. 3 (May, 2002), pp. 543-576
  179. Weinan, E; Liu, JG, Projection method III: Spatial discretization on the staggered grid, Mathematics of Computation, vol. 71 no. 237 (January, 2002), pp. 27-47, American Mathematical Society (AMS)
  180. Liu, JG; Wang, WC, An energy-preserving MAC-Yee scheme for the incompressible MHD equation, Journal of Computational Physics, vol. 174 no. 1 (November, 2001), pp. 12-37, Elsevier BV, ISSN 0021-9991
  181. Liu, JG; Xin, Z, Convergence of the point vortex method for 2-D vortex sheet, Mathematics of Computation, vol. 70 no. 234 (April, 2001), pp. 595-606, American Mathematical Society (AMS)
  182. Liu, JG; Weinan, E, Simple finite element method in vorticity formulation for incompressible flows, Mathematics of Computation, vol. 70 no. 234 (April, 2001), pp. 579-593, American Mathematical Society (AMS)
  183. Liu, JG; Weinan, E, Simple finite element method in vorticity formulation for incompressible flow, Math. Comp., vol. 69 (2001), pp. 1385-1407
  184. Liu, JG; Xin, Z, Convergence of point vortex method for 2-D vortex sheet, Math. Comp., vol. 70 no. 234 (2001), pp. 565-606
  185. Weinan, E; Liu, JG, Gauge finite element method for incompressible flows, International Journal for Numerical Methods in Fluids, vol. 34 no. 8 (December, 2000), pp. 701-710, WILEY, ISSN 0271-2091
  186. Liu, JG; Shu, CW, A High-Order Discontinuous Galerkin Method for 2D Incompressible Flows, Journal of Computational Physics, vol. 160 no. 2 (May, 2000), pp. 577-596, Elsevier BV
  187. Liu, JG; Xin, Z, Convergence of a Galerkin method for 2-D discontinuous Euler flows, Communications on Pure and Applied Mathematics, vol. 53 no. 6 (January, 2000), pp. 786-798, JOHN WILEY & SONS INC
  188. Wang, C; Liu, JG, Convergence of gauge method for incompressible flow, Mathematics of Computation, vol. 69 no. 232 (January, 2000), pp. 1385-1407
  189. Lefloch, PG; Liu, JG, Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions, Mathematics of Computation, vol. 68 no. 227 (January, 1999), pp. 1025-1055
  190. Wang, ZJ; Liu, JG; Childress, S, Connection between corner vortices and shear layer instability in flow past an ellipse, Physics of Fluids, vol. 11 no. 9 (January, 1999), pp. 2446-2448
  191. Choi, H; Liu, JG, The Reconstruction of Upwind Fluxes for Conservation Laws: Its Behavior in Dynamic and Steady State Calculations, Journal of Computational Physics, vol. 144 no. 2 (August, 1998), pp. 237-256, Elsevier BV
  192. Xu, E; Liu, JG, Pricing of mortgage-backed securities with option-adjusted spread, Managerial Finance, vol. 24 (1998), pp. 94-109
  193. E, W; Liu, JG, Finite Difference Methods for 3D Viscous Incompressible Flows in the Vorticity-Vector Potential Formulation on Nonstaggered Grids, Journal of Computational Physics, vol. 138 no. 1 (November, 1997), pp. 57-82, Elsevier BV
  194. Chen, GQ; Liu, JG, Convergence of difference schemes with high resolution for conservation laws, Mathematics of Computation, vol. 66 no. 219 (January, 1997), pp. 1027-1053
  195. Weinan, E; Liu, JG, Finite difference schemes for incompressible flows in the velocity - impulse density formulation, Journal of Computational Physics, vol. 130 no. 1 (January, 1997), pp. 67-76, Elsevier BV
  196. Weinan, E; Liu, JG, Vorticity boundary condition and related issues for finite difference schemes, Journal of Computational Physics, vol. 124 no. 2 (March, 1996), pp. 368-382, Elsevier BV
  197. Jin, S; Liu, JG, The effects of numerical viscosities: I. Slowly moving shocks, Journal of Computational Physics, vol. 126 no. 2 (January, 1996), pp. 373-389, Elsevier BV
  198. Weinan, E; Liu, JG, Essentially compact schemes for unsteady viscous incompressible flows, Journal of Computational Physics, vol. 126 no. 1 (January, 1996), pp. 122-138, Elsevier BV
  199. Weinan, E; Liu, JG, Projection method II: Godunov-Ryabenki analysis, Siam Journal on Numerical Analysis, vol. 33 no. 4 (January, 1996), pp. 1597-1621, Society for Industrial & Applied Mathematics (SIAM)
  200. Levermore, CD; Liu, JG, Large oscillations arising in a dispersive numerical scheme, Physica D: Nonlinear Phenomena, vol. 99 no. 2-3 (January, 1996), pp. 191-216, Elsevier BV
  201. Liu, JG; Xin, Z, Kinetic and viscous boundary layers for broadwell equations, Transport Theory and Statistical Physics, vol. 25 no. 3-5 (January, 1996), pp. 447-461, Informa UK Limited
  202. Jin, S; Liu, JG, Oscillations induced by numerical viscosities, Mat. Contemp., vol. 10 (1996), pp. 169-180
  203. Liu, JG; Xin, Z, Boundary layer behavior in the fluid-dynamic limit for a nonlinear model Boltzmann equation, Arch. Rat. Mech. Anal., vol. 135 no. 1 (1996), pp. 61-105, Springer Nature
  204. E, W; Liu, J-G, Finite difference schemes for incompressible flows in vorticity formulations, Esaim: Proceedings, vol. 1 (1996), pp. 181-195, E D P SCIENCES
  205. Weinan, E; Liu, JG, Projection method I: convergence and numerical boundary layers, Siam J. Numer. Anal., vol. 32 no. 4 (1995), pp. 1017-1057, Society for Industrial & Applied Mathematics (SIAM)
  206. Liu, JG; Xin, Z, Convergence of vortex methods for weak solutions to the 2-D Euler equations with vortex sheets data, Comm. Pure Appl. Math., vol. 48 no. 6 (1995), pp. 611-628
  207. Jin, S; Liu, JG, Relaxation and diffusion enhanced dispersive waves, Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, vol. 446 no. 1928 (January, 1994), pp. 555-563
  208. Lefloch, P; Liu, JG, Discrete entropy and monotonicity criteria for hyperbolic conservation laws, C.R. Acad. Sci. Paris., vol. 319 no. 8 (1994), pp. 881-886, ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER
  209. CHEN, GQ; LIU, JG, CONVERGENCE OF 2ND-ORDER SCHEMES FOR ISENTROPIC GAS-DYNAMICS, Mathematics of Computation, vol. 61 no. 204 (October, 1993), pp. 607-627, AMER MATHEMATICAL SOC
  210. Liu, JG; Xin, Z, Nonlinear stability of discrete shocks for systems of conservation laws, Archive for Rational Mechanics and Analysis, vol. 125 no. 3 (September, 1993), pp. 217-256, Springer Nature, ISSN 0003-9527
  211. Liu, J-G; Xin, Z, L 1 -Stability of Stationary Discrete Shocks, Mathematics of Computation, vol. 60 no. 201 (January, 1993), pp. 233-233, JSTOR
  212. Chen, GQ; Liu, JG, Convergence of second-order schemes for isentropic gas dynamics, Math. Comp., vol. 61 no. 204 (1993), pp. 607-629, AMER MATHEMATICAL SOC
  213. Engquist, B; Liu, JG, Numerical methods for oscillatory solutions to hyperbolic problems, Comm. Pure Appl. Math., vol. 46 no. 10 (1993), pp. 1327-1361, WILEY
  214. Liu, JG; Xin, Z, L1-stability of stationary discrete shocks, Math. Comp., vol. 60 no. 201 (1993), pp. 233-244, American Mathematical Society (AMS)

Papers Accepted

  1. P. Degond, J.-G. Liu, S. Merino-Aceituno, T. Tardiveau, Continuum dynamics of the intention field under weakly cohesive social interactions, Math. Models Methods Appl. Sci. (2016)
  2. Y. Gao, J.-G. Liu, J. Lu, Continuum limit of a mesoscopic model of step motion on vicinal surfaces, J. Nonlinear Science (2016)
Last modified: 2022/05/20