# Curriculum Vitae

## Jian-Guo Liu

### Contact information

 Box 90320, Durham, NC 27708-0320 (919) 660-2500

### Education

 Ph.D. University of California at Los Angeles 1990 M.S. Fudan University (China) 1985 B.S. Fudan University (China) 1982

### Areas of Research

Applied mathematics, nonlinear dynamics, complex system, fluid dynamics, computational sciences

### 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
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

### Conferences Organized

• 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-August 2009
• Co-Chair, Maryland, "Twelfth International Conference on Hyperbolic Problems Theory, Numerics, Applications'', June, 2008

### Professional Service

• Panelist for Yau High School Mathematics Award, 2014 - present
• Prelim committee for Hangjie Ji, 2014 - present
• Advising Math Major for Mandy Ruigi Jiang, 2014 - present
• Advising Math Major for Duke Kyeom Kim, 2014 - present
• 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
• Served on dissertation committee for Yuantong Ding, Department of Biology, 2014 - present
• Refereed for a number of journals, 2013 - present
• Member of the Steering Committee for the Tsinghua Sanya International Mathematics Forum, 2013 - present
• Member of Physics core course committee, 2013 - present
• Member of Physics Undergraduate Curriculum Committee, 2013 - present
• Chair of the international committee for the oral exam in the section Applied and Computational Mathematics for S. T. Yau College Mathematics Contests, 2013 - present
• Mentor for graduate students in Mathematics, September 1, 2012 - present
• Promotion and tenure external evaluators for various universities, 1 January 2012
• Managing Editor for "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
• Prelim exam committee for Qiang Ren, Department of Electrical and Computer Engineering, November 2014
• Ph.D. dissertation committee for Ethan Elliott, November 2014
• Ph.D. dissertation committee for Di-Lun Yang, September 1, 2011 - 2014
• Advising Math Major for Siyang Sun, December 2013
• Advising Math Major for Xiaoyang Zhuang, December 2013
• Advising Math Major for Kevin Rozell, December 2013
• Math honors theses advising for Kara Karpman, December 2013
• Preliminary examination committee for Joey Schmitt, December 2013
• Ph.D. defense committee for Luis Tobon, December 2013
• Co-organized SIAM Conference on Analysis of Partial Differential Equations, mini-symposium: Asymptotically Preserving Numerical Methods for Time-Depe, Co-organized SIAM Conference on Analysis of Partial Differential Equations, mini-symposium: Asymptotically Preserving Numerical Methods for Time-Depe., December 2013
• Initialed and signed a MOU between The Math department at Duke and the Mathematical Science Center (MSC), Tsinghua University, December 2013
• Graduate assessment committee, September 1, 2011 - 2013
• Ph.D. dissertation committee for Huaixiu Zheng, January 13, 2011 - 2013
• Committee member, Thesis Defense Committee for Yi Li, November 27, 2012
• Chair for Committee to Review Prof. Jim Nolen, September 1, 2011 - August 31, 2012
• Committee to Review Prof. Steffen Bass, September 1, 2011 - August 31, 2012
• Written Analysis Qual Exam Committee, September 1, 2010 - August 31, 2012
• Oral qualifying exam committee for Jingxian Huang, May 05, 2012
• Ph.D. dissertation committee for Chingyun Cheng, March 5, 2012 - 2012
• Advising Math Major for Scott Cara, 2012
• Advising Math Major for Darius Brown, 2012
• Chair, Physics Computing Committee, September 1, 2009 - August 30, 2010
• Oral qualifying exam committee for Ioannis Sgouralis, June 14, 2010
• Preliminary Examination Committee for Jiefu Chen,, November 12, 2009
• Assistant Research Professor Searching Committee, 2009
• Editorial Board, "Journal of Information and Computational Science'', 2005 - 2008
• Served on Panel: National Science Foundation, CFD, 2007
• Organizer Committee, Maryland, CSCAMM Workshop on Analytical and Computational Challenges of Incompressible Flows at High Reynolds Number, October, 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 25, 2005

### Selected Recent Invited Talks

• 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 .
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 .
3. Dynamics in Models of Coarsening, Coagulation, Condensation and Quantization, edited by W. Bao and J.-G. Liu (2007), World Scientific .
Papers Published
1. Liu, J-G; 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 .
2. Li, L; Liu, JG, p-Euler equations and p-Navier-Stokes equations, Journal of Differential Equations (January, 2018) .
3. Li, L; Liu, J-G; Lu, J, Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem, Journal of Statistical Physics, vol. 169 no. 2 (October, 2017), pp. 316-339 .
4. Liu, J-G; 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 .
5. Gao, Y; Ji, H; Liu, J-G; 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 .
6. Gao, Y; Liu, J-G; 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 .
7. Gao, Y; Liu, J-G; 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 .
8. Liu, J-G; 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 .
9. Degond, P; Liu, J-G; Merino-Aceituno, S; Tardiveau, T, Continuum dynamics of the intention field under weakly cohesive social interaction, Mathematical Models & Methods in Applied Sciences, vol. 27 no. 01 (January, 2017), pp. 159-182 .
10. Gao, Y; Liu, J-G, 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 .
11. Liu, J-G; 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 .
12. Huang, H; Liu, J-G, Discrete-in-time random particle blob method for the Keller–Segel equation and convergence analysis, Communications in Mathematical Sciences, vol. 15 no. 7 (2017), pp. 1821-1842 .
13. Degond, P; Herty, M; Liu, J-G, Mean-field games and model predictive control, Communications in Mathematical Sciences, vol. 15 no. 5 (2017), pp. 1403-1422 .
14. Li, L; Liu, J-G, A note on deconvolution with completely monotone sequences and discrete fractional calculus, Quarterly of Applied Mathematics (2017), pp. 1-1 .
15. Coquel, F; Jin, S; Liu, J-G; Wang, L, Entropic sub-cell shock capturing schemes via Jin-Xin relaxation and Glimm front sampling for scalar conservation laws, Mathematics of Computation (2017), pp. 1-1 .
16. Liu, J-G; Wang, L; Zhou, Z, Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations, Mathematics of Computation (2017), pp. 1-1 .
17. Liu, J-G; Cong, W, Uniform $L^{\infty}$ boundedness for a degenerate parabolic-parabolic Keller-Segel model, Discrete and Continuous Dynamical Systems - Series B, vol. 22 no. 2 (December, 2016), pp. 307-338 .
18. Huang, H; Liu, J-G, A note on Monge–Ampère Keller–Segel equation, Applied Mathematics Letters, vol. 61 (November, 2016), pp. 26-34 .
19. Huang, H; Liu, J-G, Error estimates of the aggregation-diffusion splitting algorithms for the Keller-Segel equations, Discrete and Continuous Dynamical Systems - Series B, vol. 21 no. 10 (November, 2016), pp. 3463-3478 .
20. Liu, J-G; Huang, H, 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 (September, 2016), pp. 715-748 .
21. Liu, J-G; Cong, W, A degenerate $p$-Laplacian Keller-Segel model, Kinetic and Related Models, vol. 9 no. 4 (September, 2016), pp. 687-714 .
22. Liu, J-G; Wang, J, A Note on L ∞ $L^{\infty}$ -Bound and Uniqueness to a Degenerate Keller-Segel Model, Acta Applicandae Mathematicae, vol. 142 no. 1 (April, 2016), pp. 173-188 .
23. Herschlag, G; Liu, J-G; 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 .
24. Liu, J-G; Pego, RL, On generating functions of Hausdorff moment sequences, Transactions of the American Mathematical Society, vol. 368 no. 12 (February, 2016), pp. 8499-8518 .
25. 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 .
26. Chen, J; Liu, J-G; 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 .
27. Liu, J-G; Xu, X, Existence Theorems for a Multidimensional Crystal Surface Model, SIAM Journal on Mathematical Analysis, vol. 48 no. 6 (January, 2016), pp. 3667-3687 .
28. 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 .
29. J.-G. Liu and R. Yang, Propagation of chaos for large Brownian particle system with Coulomb interaction, Research in the Mathematical Sciences, vol. 3 no. 40 (2016) .
30. Y. Duan and J.-G. Liu, Error estimate of the particle method for the b-equation, Methods and Applications of Analysis, vol. 23 (2016), pp. 119-154 .
31. J.-G. Liu and Y. Zhang, Convergence of stochastic interacting particle systems in probability under a Sobolev norm, Annals of Mathematical Sciences and Applications, vol. 1 (2016), pp. 251-299 .
32. Xue, Y; Wang, C; Liu, J-G, 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 (December, 2015), pp. 1189-1216 .
33. Lu, J; Liu, J-G; 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 .
34. 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 (January, 2015), pp. 63-115 .
35. 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 .
36. Herschlag, G; Liu, J-G; 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 .
37. Degond, P; Liu, J-G; Ringhofer, C, Evolution of wealth in a non-conservative economy driven by local Nash equilibria, Philosophical Transactions A, vol. 372 no. 2028 (October, 2014), pp. 20130394-20130394 .
38. Goudon, T; Jin, S; Liu, JG; 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 (May, 2014), pp. 81-102 .
39. Duan, Y; Liu, JG, Convergence analysis of the vortex blob method for the b-equation, Discrete and Continuous Dynamical Systems, vol. 34 no. 5 (May, 2014), pp. 1995-2011 .
40. 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 (January, 2014), pp. 1051-1084 .
41. Degond, P; Herty, M; Liu, J-G, Flow on Sweeping Networks, Multiscale Modeling & Simulation, vol. 12 no. 2 (January, 2014), pp. 538-565 .
42. Chen, X; Li, X; Liu, J-G, 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 (2014), pp. 1579-1601 .
43. Johnston, H; Wang, C; Liu, J-G, A Local Pressure Boundary Condition Spectral Collocation Scheme for the Three-Dimensional Navier–Stokes Equations, Journal of Scientific Computing, vol. 60 no. 3 (2014), pp. 612-626 .
44. 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, HYPERBOLIC PROBLEMS: THEORY, NUMERICS, APPLICATIONS, vol. 8 (2014), pp. 179-192 .
45. Zou, C; Liu, J-G; Bian, S, Ultra-contractivity for Keller-Segel model with diffusion exponent $m>1-2/d$, Kinetic and Related Models, vol. 7 no. 1 (December, 2013), pp. 9-28 .
46. 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 .
47. 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 .
48. P. Degond, J.-G, Liu, S. Motsch, V. Panferov, Hydrodynamic models of self-organized dynamics: derivation and existence theory, Methods Anal. Appl., vol. 20 (2013), pp. 89-114 .
49. 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 .
50. 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 .
51. 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 .
52. Chae, D; Degond, P; Liu, J-G, Well-posedness for Hall-magnetohydrodynamics, Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, vol. 31 no. 3 (2013), pp. 555-565 .
53. Chen, X; Liu, J-G, Analysis of polymeric flow models and related compactness theorems in weighted spaces, SIAM Journal on Mathematical Analysis, vol. 45 no. 3 (2013), pp. 1179-1215 .
54. Bian, S; Liu, J-G, Dynamic and Steady States for Multi-Dimensional Keller-Segel Model with Diffusion Exponent m > 0, Communications in Mathematical Physics, vol. 323 no. 3 (2013), pp. 1017-1070 .
55. Goudon, T; Jin, S; Liu, J-G; Yan, B, Asymptotic-preserving schemes for kinetic-fluid modeling of disperse two-phase flows, Journal of Computational Physics, vol. 246 (2013), pp. 145-164 .
56. Chen, X; Liu, J-G, 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 (2013), pp. 2764-2802 .
57. 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 .
58. Chae, D; Liu, J-G, Blow-up, Zero α Limit and the Liouville Type Theorem for the Euler-Poincaré Equations, Communications in Mathematical Physics, vol. 314 no. 3 (2012), pp. 671-687 .
59. Chen, X; Liu, J-G, Two nonlinear compactness theorems in L p(0,T;B), Applied Mathematics Letters, vol. 25 no. 12 (2012), pp. 2252-2257 .
60. Chen, L; Liu, J-G; Wang, J, Multidimensional degenerate Keller-Segel system with critical diffusion exponent 2n/(n + 2), SIAM Journal on Mathematical Analysis, vol. 44 no. 2 (2012), pp. 1077-1102 .
61. Frouvelle, A; Liu, J-G, Dynamics in a kinetic model of oriented particles with phase transition, SIAM Journal on Mathematical Analysis, vol. 44 no. 2 (2012), pp. 791-826 .
62. Carrillo, JA; Chen, L; Liu, J-G; Wang, J, A note on the subcritical two dimensional Keller-Segel system, Acta Applicandae Mathematicae, vol. 119 no. 1 (2012), pp. 43-55 .
63. Degond, P; Liu, J-G, Hydrodynamics of self-alignment interactions with precession and derivation of the Landau-Lifschitz-Gilbert equation, Mathematical Models & Methods in Applied Sciences, vol. 22 no. SUPPL.1 (2012), pp. 1114001-18 .
64. Chertock, A; Liu, J-G; Pendleton, T, Convergence of a particle method and global weak solutions of a family of evolutionary PDEs, SIAM Journal on Numerical Analysis, vol. 50 no. 1 (2012), pp. 1-21 .
65. Haack, J; Jin, S; Liu, J-G, An all-speed asymptotic-preserving method for the isentropic Euler and Navier-Stokes equations, Communications in computational physics, vol. 12 no. 4 (2012), pp. 955-980 .
66. Degond, P; Frouvelle, A; Liu, J-G, Macroscopic Limits and Phase Transition in a System of Self-propelled Particles, Journal of Nonlinear Science, vol. 23 no. 3 (2012), pp. 1-30 .
67. Jin, S; Liu, J-G; Wang, L, A domain decomposition method for semilinear hyperbolic systems with two-scale relaxations, Math. Comp., vol. 82 (2011), pp. 749-779 .
68. Liu, J-G; Lorz, A, A coupled chemotaxis-fluid model: Global existence, Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, vol. 28 no. 5 (2011), pp. 643-652 .
69. Acheritogaray, M; Degond, P; Frouvelle, A; Liu, J-G, Kinetic formulation and global existence for the hall-magneto-hydrodynamics system, Kinetic and Related Models, vol. 4 no. 4 (2011), pp. 901-918 .
70. Zheng, W; Gao, H; Liu, J-G; Zhang, Y; Ye, Q; Swank, C, General solution to gradient-induced transverse and longitudinal relaxation of spins undergoing restricted diffusion, Physical Review A - Atomic, Molecular, and Optical Physics, vol. 84 no. 5 (2011), pp. 053411-8 .
71. Huang, Y-L; Liu, J-G; Wang, W-C, An FFT based fast poisson solver on spherical shells, Communications in computational physics, vol. 9 no. 3 (2011), pp. 649-667 .
72. Liu, J-G; Liu, J; Pego, RL, Stable and accurate pressure approximation for unsteady incompressible viscous flow, Journal of Computational Physics, vol. 229 no. 9 (2010), pp. 3428-3453 .
73. Liu, J-G; Mieussens, L, Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit, SIAM Journal on Numerical Analysis, vol. 48 no. 4 (2010), pp. 1474-1491 .
74. Liu, J-G; Pego, R, Stable discretization of magnetohydrodynamics in bounded domains, Commun. Math. Sci., vol. 8 no. 1 (2010), pp. 234-251 .
75. Liu, J-G; Pego, RL, Stable discretization of magnetohydrodynamics in bounded domains, Communications in Mathematical Sciences, vol. 8 no. 1 (2010), pp. 235-251 .
76. Liu, J-G; 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 (2009), pp. 743-768 .
77. Liu, J-G; Wang, W-C, Characterization and regularity for axisymmetric solenoidal vector fields with application to navier-stokes equation, SIAM Journal on Mathematical Analysis, vol. 41 no. 5 (2009), pp. 1825-1850 .
78. Ha, S-Y; Liu, J-G, A simple proof of the Cucker-Smale flocking dynamics and mean-field limit, Communications in Mathematical Sciences, vol. 7 no. 2 (2009), pp. 297-325 .
79. Hsia, C-H; Liu, J-G; Wang, C, Structural stability and bifurcation for 2D incompressible ows with symmetry, Meth. Appl. Anal., vol. 15 (2008), pp. 495-512 .
80. Lin, P; Liu, J-G; 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 (2008), pp. 398-419 .
81. Liu, J-G; Wang, C, A fourth order numerical method for the primtive equations formulated in mean vorticity, Communications in computational physics, vol. 4 no. 1 (2008), pp. 26-55 .
82. Degond, P; Liu, J-G; Vignal, M-H, Analysis of an asymptotic preserving scheme for the Euler-Poisson system in the quasineutral limit, SIAM Journal on Numerical Analysis, vol. 46 no. 3 (2008), pp. 1298-1322 .
83. Lu, X; Lin, P; Liu, J-G, Analysis of a sequential regularization method for the unsteady Navier-Stokes equations, Mathematics of Computation, vol. 77 no. 263 (2008), pp. 1467-1494 .
84. 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. .
85. Liu, J-G; Liu, J; Pego, RL, Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate, Communications on Pure & Applied Mathematics, vol. 60 no. 10 (2007), pp. 1443-1487 .
86. Liu, J-G; 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 .
87. 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 .
88. Antman, SS; Liu, J-G, Basic themes and pretty problems of nonlinear solid mechanics, Milan Journal of Mathematics, vol. 75 no. 1 (2007), pp. 135-176 .
89. Moore, J; Cheng, Z; Hao, J; Guo, G; Liu, J-G; Lin, C; Yu, L, 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 (2007), pp. 10173-10182(published on Web 10/30/2007.) .
90. 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. .
91. Degond, P; Liu, J-G; Mieussens, L, Macroscopic fluid models with localized kinetic upscaling effects, Multiscale Modeling & Simulation, vol. 5 no. 3 (2006), pp. 940-979 .
92. Moore, J; Liu, J-G; Zhou, K; Yu, L, Effects of genotype and environment on the antioxidant properties of hard winter wheat bran, Journal of Agricultural and Food Chemistry, vol. 54 no. 15 (2006), pp. 5313-5322 .
93. Liu, J-G; Wang, W-C, Convergence analysis of the energy and helicity preserving scheme for axisymmetric flows, SIAM Journal on Numerical Analysis, vol. 44 no. 6 (2006), pp. 2456-2480 .
94. Liu, J-G; Samelson, R; Wang, C, Global weak solution of planetary geostrophic equations with inviscid geostrophic balance, Applicable Analysis, vol. 85 (2006), pp. 593-605 .
95. Liu, J-G; Wang, W-C, Energy and helicity preserving schemes for hydro- and magnetohydro-dynamics flows with symmetry, Journal of Computational Physics, vol. 200 no. 1 (2004), pp. 8-33 .
96. Lin, H-E; Liu, J-G; Xu, W-Q, Effects of small viscosity and far field boundary conditions for hyperbolic systems, Communications on Pure and Applied Analysis, vol. 3 no. 2 (2004), pp. 267-290 .
97. Liu, J-G; Xu, W-Q, Far field boundary condition for convection diffusion equation at zero viscosity limit, Quarterly of Applied Mathematics, vol. 62 no. 1 (2004), pp. 27-52 .
98. Wang, C; Liu, J-G; Johnston, H, Analysis of a fourth order finite difference method for the incompressible Boussinesq equations, Numerische Mathematik, vol. 97 no. 3 (2004), pp. 555-594 .
99. Li, B; Liu, J-G, Eptaxial growth without slope selection: energetics, coarsening, and dynamic scaling, J. Nonlinear Sci., vol. 14 no. 5 (2004), pp. 429-451 .
100. Johnston, H; Liu, J-G, Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term, Journal of Computational Physics, vol. 199 no. 1 (2004), pp. 221-259 .
101. Ghil, M; Liu, J-G; 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 (2004), pp. 149-173 .
102. Liu, J-G; 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 .
103. Liu, J-G; Wang, C, High order finite difference methods for unsteady incompressible flows in multi-connected domains, Computers and Fluids, vol. 33 no. 2 (2004), pp. 223-255 .
104. Li, B; Liu, J-G, Epitaxial growth without slope selection: Energetics, coarsening, and dynamic scaling, Journal of Nonlinear Science, vol. 14 no. 5 (2004), pp. 429-451 .
105. Wang, C; Liu, J-G, Fourth order convergence of a compact difference solver for incompressible flow, Commun. Appl. Anal., vol. 7 (2003), pp. 171-191 .
106. Wang, C; Liu, J-G, Positivity property of second-order flux-splitting schemes for the compressible Euler equations, Discrete and Continuous Dynamical Systems - Series B, vol. 3 no. 2 (2003), pp. 201-228 .
107. Chainais-Hillairet, C; Liu, J-G; Peng, Y-J, Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis, Mathematical Modelling and Numerical Analysis, vol. 37 no. 2 (2003), pp. 319-338 .
108. Duraisamy, K; Baeder, JD; Liu, J-G, Concepts and Application of Time-Limiters to High Resolution Schemes, Journal of Scientific Computing, vol. 19 no. 1-3 (2003), pp. 139-162 .
109. Weinan, E; Liu, J-G, Gauge method for viscous incompressible flows, Comm. Math. Sci., vol. 1 (2003), pp. 317-332 .
110. Li, B; Liu, J-G, Thin film epitaxy with or without slope selection, European Journal of Applied Mathematics, vol. 14 no. 6 (2003), pp. 713-743 .
111. Chern, I-L; Liu, J-G; Wang, W-C, Accurate evaluation of electrostatics for macromolecules in solution, Methods and Applications of Analysis, vol. 10 (2003), pp. 309-328 .
112. Liu, J-G; Wang, C; Johnston, H, A Fourth Order Scheme for Incompressible Boussinesq Equations, Journal of Scientific Computing, vol. 18 no. 2 (2003), pp. 253-285 .
113. Wang, C; Liu, J-G, Analysis of finite difference schemes for unsteady Navier-Stokes equations in vorticity formulation, Numerische Mathematik, vol. 91 no. 3 (2002), pp. 543-576 .
114. Weinan, E; Liu, J-G, Projection method III: Spatial discretization on the staggered grid, Mathematics of Computation, vol. 71 no. 237 (2002), pp. 27-47 .
115. Johnston, H; Liu, J-G, Finite difference schemes for incompressible flow based on local pressure boundary conditions, Journal of Computational Physics, vol. 180 no. 1 (2002), pp. 120-154 .
116. Liu, J-G; Xin, Z, Convergence of the point vortex method for 2-D vortex sheet, Mathematics of Computation, vol. 70 no. 234 (2001), pp. 595-606 .
117. Liu, J-G; Weinan, E, Simple finite element method in vorticity formulation for incompressible flows, Mathematics of Computation, vol. 70 no. 234 (2001), pp. 579-593 .
118. Liu, J-G; Wang, W-C, An energy-preserving MAC-Yee scheme for the incompressible MHD equation, Journal of Computational Physics, vol. 174 no. 1 (2001), pp. 12-37 .
119. Liu, J-G; Weinan, E, Simple finite element method in vorticity formulation for incompressible flow, Math. Comp., vol. 69 (2001), pp. 1385-1407 .
120. Liu, J-G; Xin, Z, Convergence of point vortex method for 2-D vortex sheet, Math. Comp., vol. 70 no. 234 (2001), pp. 565-606 .
121. Liu, J-G; Xin, Z, Convergence of a Galerkin method for 2-D discontinuous Euler flows, Communications on Pure and Applied Mathematics, vol. 53 no. 6 (2000), pp. 786-798 .
122. Liu, J-G; Shu, C-W, A High-Order Discontinuous Galerkin Method for 2D Incompressible Flows, Journal of Computational Physics, vol. 160 no. 2 (2000), pp. 577-596 .
123. Wang, C; Liu, J-G, Convergence of gauge method for incompressible flow, Mathematics of Computation, vol. 69 no. 232 (2000), pp. 1385-1407 .
124. Weinan, E; Liu, J-G, Gauge finite element method for incompressible flows, International Journal for Numerical Methods in Fluids, vol. 34 no. 8 (2000), pp. 701-710 .
125. Lefloch, PG; Liu, J-G, Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions, Mathematics of Computation, vol. 68 no. 227 (1999), pp. 1025-1055 .
126. 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 (1999), pp. 2446-2448 .
127. Xu, E; Liu, J-G, Pricing of mortgage-backed securities with option-adjusted spread, Managerial Finance, vol. 24 (1998), pp. 94-109 .
128. Choi, H; Liu, J-G, The Reconstruction of Upwind Fluxes for Conservation Laws: Its Behavior in Dynamic and Steady State Calculations, Journal of Computational Physics, vol. 144 no. 2 (1998), pp. 237-256 .
129. Weinan, E; Liu, J-G, 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 (1997), pp. 57-82 .
130. Chen, G-Q; Liu, J-G, Convergence of difference schemes with high resolution for conservation laws, Mathematics of Computation, vol. 66 no. 219 (1997), pp. 1027-1053 .
131. Weinan, E; Liu, J-G, Finite difference schemes for incompressible flows in the velocity - impulse density formulation, Journal of Computational Physics, vol. 130 no. 1 (1997), pp. 67-76 .
132. Jin, S; Liu, J-G, Oscillations induced by numerical viscosities, Mat. Contemp., vol. 10 (1996), pp. 169-180 .
133. Jin, S; Liu, J-G, The effects of numerical viscosities: I. Slowly moving shocks, Journal of Computational Physics, vol. 126 no. 2 (1996), pp. 373-389 .
134. Weinan, E; Liu, J-G, Vorticity boundary condition and related issues for finite difference schemes, Journal of Computational Physics, vol. 124 no. 2 (1996), pp. 368-382 .
135. Weinan, E; Liu, J-G, Essentially compact schemes for unsteady viscous incompressible flows, Journal of Computational Physics, vol. 126 no. 1 (1996), pp. 122-138 .
136. Weinan, E; Liu, J-G, Projection method II: Godunov-Ryabenki analysis, SIAM Journal on Numerical Analysis, vol. 33 no. 4 (1996), pp. 1597-1621 .
137. Levermore, CD; Liu, J-G, Large oscillations arising in a dispersive numerical scheme, Physica D: Nonlinear Phenomena, vol. 99 no. 2-3 (1996), pp. 191-216 .
138. Liu, J-G; Xin, Z, Kinetic and viscous boundary layers for broadwell equations, Transport Theory and Statistical Physics, vol. 25 no. 3-5 (1996), pp. 447-461 .
139. Liu, J-G; Xin, Z, Boundary layer behavior in the fluid-dynamic limit for a nonlinear model Boltzmann equation, Arch. Rat. Mech. Anal., vol. 135 (1996), pp. 61-105 .
140. Weinan, E; Liu, J-G, Projection method I: convergence and numerical boundary layers, SIAM J. Numer. Anal., vol. 32 (1995), pp. 1017-1057 .
141. Liu, J-G; 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 (1995), pp. 611-628 .
142. Lefloch, P; Liu, J-G, Discrete entropy and monotonicity criteria for hyperbolic conservation laws, C.R. Acad. Sci. Paris., vol. 319 (1994), pp. 881-886 .
143. Jin, S; Liu, J-G, Relaxation and diffusion enhanced dispersive waves, Proceedings of The Royal Society of London, Series A: Mathematical and Physical Sciences, vol. 446 no. 1928 (1994), pp. 555-563 .
144. Chen, G-Q; Liu, J-G, Convergence of second-order schemes for isentropic gas dynamics, Math. Comp., vol. 61 (1993), pp. 607-629 .
145. Engquist, B; Liu, J-G, Numerical methods for oscillatory solutions to hyperbolic problems, Comm. Pure Appl. Math., vol. 46 (1993), pp. 1327-1361 .
146. Liu, J-G; Xin, Z, L1-stability of stationary discrete shocks, Math. Comp., vol. 60 (1993), pp. 233-244 .
147. Liu, J-G; Xin, Z, Nonlinear stability of discrete shocks for systems of conservation laws, Archive for Rational Mechanics and Analysis, vol. 125 no. 3 (1993), pp. 217-256 .
Papers Accepted
1. Degond, P; Liu, J-G; Pego, RL, Coagulation–Fragmentation Model for Animal Group-Size Statistics, Journal of Nonlinear Science, vol. 27 no. 2 (April, 2017), pp. 379-424 .
2. Huang, H; Liu, J-G, Error estimate of a random particle blob method for the Keller-Segel equation, Mathematics of Computation, vol. 86 no. 308 (February, 2017), pp. 2719-2744 .
3. Liu, J-G; Wang, J, Global existence for a thin film equation with subcritical mass, Discrete and Continuous Dynamical Systems - Series B, vol. 22 no. 4 (February, 2017), pp. 1461-1492 .
4. Liu, J-G; Yang, R, A random particle blob method for the Keller-Segel equation and convergence analysis, Mathematics of Computation, vol. 86 no. 304 (May, 2016), pp. 725-745 .
5. 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) .
6. Y. Gao, J.-G. Liu, J. Lu, Continuum limit of a mesoscopic model of step motion on vicinal surfaces, J. Nonlinear Science (2016) .