Curriculum Vitae

Jian-Guo Liu

Duke University, Box 90320
Durham, NC 27708-0320
USA 		919-660-2546 (office)
919-929-0180 (home)
(email)
Education

PhDUniversity of California, Los Angeles1990
MSFudan University1985
BSFudan University1982
Areas of Research

Numerical Analysis, Partial Differential Equations, Computational Fluid Dynamics

Areas of Interest

Numerical Analysis
Partial Differential Equations
Computational Fluid Dynamics

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
Recent Grant Support

Conferences Organized

Organizer Committee, IMA Workshop on Analysis and Computation of Incompressible Fluid Flow, February, 2010  
Organizer Committee, Singapore, Two Month Program on Mathematical Theory and Numerical Methods for Computational Materials Simulation and Design, 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

Dept Committee
Graduate assessment committee, Physics, 2011 - present  
Written Analysis Qual Exam Committee, 2010 - present  
Preliminary Examination Committee for Chingyun Cheng, Physics, December 2011  
Thesis Defense Committee for Matt Bowen, Mathematics, November 2011  
Ph.D. dissertation committee for Di-Lun Yang, Physics, 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
exterior doctoral committee for Baver Okutmustur, University Paris VI, 2010  
Served on Panel: National Science Foundation, CFD, 2007, December 2007  
NSF Reviews And Panels
panelist, NSF Numerical Methods (P100833) panel, March, 2010  
Math Community Services
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, August-September, 2010  
Editorial Board, "Journal of Information and Computational Science'', 2005 - 2008  
Selected Recent Invited Talks

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. W. Zheng, H. Gao, J.-G.-Liu, Y. Zhang, Q. Ye and C. Swank, General solution to gradient-induced transverse and longitudinal relaxation of spins undergoing restricted diffusion, Phys. Rev. A, vol. 84 (2011), pp. 053411-8
  2. M. Acheritogaray, P. Degond, A. Frouvelle, and J.-G. Liu, Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system, Kinetic and Related Models, vol. 4 (2011), pp. 901-918
  3. J.-G. Liu and A. Lorz, A coupled chemotaxis-fluid model: Global existence, Ann. I. H. Poincare, AN, vol. 28 (2011), pp. 643-652
  4. Y.-L. Huang, J.-G. Liu and W.-C. Wang, An FFT based fast Poisson solver on spherical shells, Commun. Comput. Phy., vol. 9 (2011), pp. 649-667
  5. J.-G. Liu, Jie Liu and R. Pego, Stable and accurate pressure approximation for unsteady incompressible viscous flow, J. Comput. Phys., vol. 229 (2010), pp. 3428-3453
  6. J.-G. Liu and L. Mieussens, Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit, SIAM J. Numer. Anal., vol. 48 (2010), pp. 1474-1491
  7. J.-G. Liu and R. Pego, Stable discretization of magnetohydrodynamics in bounded domains, Commun. Math. Sci., vol. 8 (2010), pp. 234-251
  8. S.-Y. Ha and J.-G. Liu, A simple proof of the Cucker-Smale flocking dynamics and mean-field limit, Commun. Math. Sci., vol. 7 (2009), pp. 297-325
  9. J.-G. Liu and W.-C. Wang, Characterization and regularity for axisymmetric solenoidal vector elds with application to Navier-Stokes equation, SIAM J. Math. Anal., vol. 41 (2009), pp. 1825-1850
  10. J.-G. Liu, J. Liu and R. Pego, Error estimates for finite-element Navier-Stokes solvers without standard inf-sup conditions, Chin. Ann. Math. Ser. B, vol. 30 (2009), pp. 743-768
  11. X. Lu, P. Lin and J.-G. Liu, Analysis of a sequential regularization method for the unsteady Navier-Stokes equations, Math. Comp., vol. 77 (2008), pp. 1467-1494
  12. P. Degond, J.-G. Liu and M.H. Vignal, Analysis of an asymptotic preserving scheme for the Euler-Poisson system in the quasineutral limit, SIAM J. Num. Anal., vol. 46 (2008), pp. 1298-1322
  13. J.-G. Liu and C. Wang, A fourth order numerical method for the primitive equations formulated in mean vorticity, Commun. Comput. Phys., vol. 4 (2008), pp. 26-55
  14. P. Lin, J.-G. Liu and X. Lu, Long time numerical solutyion of the Navier-Stokes equations based on a sequential regularization formulation, SIAM J. Sci. Comput., vol. 31 (2008), pp. 398-419
  15. C.-H. Hsia, J.-G. Liu and C. Wang, Structural stability and bifurcation for 2D incompressible ows with symmetry, Meth. Appl. Anal., vol. 15 (2008), pp. 495-512
  16. 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.
  17. J. Moore, Z. Cheng, J. Hao, G. Guo, J.-G. Liu, C. Lin and L. Yu, Effects of solid-state yeast treatment on the antioxidant properties and protein and fiber compositions of common hard wheat bran, J Agric Food Chem (2007) (published on Web 10/30/2007.)
  18. S.S. Antman and J.-G. Liu, Basic themes and pretty problems of nonlinear solid mechanics, Milan J. Math., vol. 75 (2007), pp. 135-176
  19. J.-G. Liu, J. Liu and R. Pego, 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
  20. P. Degond, S. Jin, and J.G. Liu, 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
  21. J.-G. Liu, R. Samelson and C. Wang, Global weak solution of planetary geostrophic equations with inviscid geostrophic balance, Applicable Analysis, vol. 85 (2006), pp. 593 - 605
  22. J.-G. Liu and W.C. Wang, Convergence analysis of the energy and helicity preserving scheme for axisymmetric flows, SIAM J. Numer. Anal., vol. 44 (2006), pp. 2456-2480
  23. P. Degond, J.-G. Liu, and L. Mieussens, Macroscopic fluid models with localized kinetic upscaling effects, Multiscale Model. Simul., vol. 5 (2006), pp. 940--979
  24. 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.
  25. J. Moore, J.-G. Liu, K. Zhou, S. Haley, and L. Yu, Effects of genotype and environment on the antioxidant properties of hard winter wheat bran, J Agric Food Chem, vol. 54 (2006), pp. 5313-5322
  26. J.-G. Liu and C. Wang, High order finite difference method for unsteady incompressible flow on multi-connected domain in vorticity-stream function formulation, Computer and Fluids, vol. 33 (2004), pp. 223-255
  27. M. Ghil, J.-G. Liu, C. Wang and S. Wang, Boundary-layer separation and adverse pressure gradient for 2-D viscous incompressible flow, Physica D, vol. 197 (2004), pp. 149--173
  28. H. Johnston and J.-G. Liu, Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term, J. Comput. Phys., vol. 188 (2004), pp. 221-259
  29. J.-G. Liu and W.-C. Wang, Energy and helicity preserving schemes for hydro- and magneto-hydrodynamics flows with symmetry, J. Comput. Phys., vol. 200 (2004), pp. 8-33
  30. B. Li and J.-G. Liu, Eptaxial growth without slope selection: energetics, coarsening, and dynamic scaling, J. Nonlinear Sci., vol. 14 (2004), pp. 429--451
  31. C. Wang, J.-G. Liu and H. Johnston, Analysis of a fourth order finite difference method for the incompressible Boussinesq equations, Numer. Math., vol. 97 (2004), pp. 555--594
  32. J.-G. Liu, and W.-Q. Xu, Far field boundary condition for convection diffusion equation at zero viscosity limit, Q APPL MATH, vol. 62 (2004), pp. 27-52
  33. H.-E. Lin, J.-G. Liu, and W.-Q. Xu, Effects of small viscosity and far field boundary conditions for hyperbolic systems, Comm. Pure Applied Anal., vol. 3 (2004), pp. 267-290
  34. J.-G. Liu, C. Wang and H. Johnston, A fourth order compact scheme for incompressible Boussinesq equations, J. Sci. Comput., vol. 18 (2003), pp. 253-285
  35. I.-L. Chern, J.-G. Liu and W.-C. Wang, Accurate evaluation of electrostatics for macromolecules in solution, Methods and Applications of Analysis, vol. 10 (2003), pp. 309-328
  36. B. Li and J.-G. Liu, Thin film epitaxy with or without slope selection, European J. Applied Math., vol. 14 (2003), pp. 713-743
  37. Weinan E and J.-G. Liu, Gauge method for viscous incompressible flows, Comm. Math. Sci., vol. 1 (2003), pp. 317--332
  38. K. Duraisamy, J.D. Baeder and J.-G. Liu, Concepts and application of time limiters to high resolution schemes, J. Sci. Comput., vol. 19 (2003), pp. 139-162
  39. C. Chainais-Hillairet, J.-G. Liu and Y.-J. Peng, Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis, Math. Model. Numer. Anal., vol. 37 (2003), pp. 319-338
  40. C. Wang and J.-G. Liu, Positivity property of second-order flux-splitting schemes for the compressible Euler equations, Discrete Contin. Dyn. Syst. Ser. B., vol. 3 (2003), pp. 201-228
  41. C. Wang and J.-G. Liu, Fourth order convergence of a compact difference solver for incompressible flow, Commun. Appl. Anal., vol. 7 (2003), pp. 171-191
  42. H. Johnston and J.-G. Liu, Finite difference schemes for incompressible flow based on local pressure boundary condition, J. Comput. Phys., vol. 180 (2002), pp. 120-154
  43. Weinan E and J.-G. Liu, Projection method III: spatial discretization on the staggered grid, Math. Comp., vol. 71 (2002), pp. 27-47
  44. C. Wang and J.-G. Liu, Analysis of finite difference schemes for unsteady Navier-Stokes equations in vorticity formulation, Numer. Math., vol. 91 (2002), pp. 543-576
  45. J.-G. Liu and Z. Xin, Convergence of point vortex method for 2-D vortex sheet, Math. Comp., vol. 70 (2001), pp. 565-606
  46. J.-G. Liu and Weinan E, Simple finite element method in vorticity formulation for incompressible flow, Math. Comp., vol. 69 (2001), pp. 1385-1407
  47. J.-G. Liu and W.C. Wang, An energy preserving MAC-Yee scheme for the incompressible MHD equation, J. Comput. Phys., vol. 174 (2001), pp. 12-37
  48. Weinan E and J.-G. Liu, Gauge finite element method for incompressible flows, Int. J. Num. Meth. Fluids, vol. 34 (2000), pp. 701-710
  49. C. Wang and J.-G. Liu, Convergence of gauge method for incompressible flow, Math. Comp., vol. 69 (2000), pp. 1385-1407
  50. J.-G. Liu and C.-W. Shu, A high order discontinuous Galerkin method for incompressible flows, J. Comput. Phys., vol. 160 (2000), pp. 577-596
  51. J.-G. Liu and Z. Xin, Convergence of a Galerkin method for 2-D discontinuous Euler flows, Comm. Pure Appl. Math., vol. 53 (2000), pp. 786-798
  52. Z.J. Wang, S. Childress and J.-G. Liu, Connection between corner vortices and shear layer instability in flow past an ellipse, Phys. Fluids., vol. 11 (1999), pp. 2446-2448
  53. P. Lefloch and J.-G. Liu, Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions, Math. Comp., vol. 68 (1999), pp. 1025-1055
  54. H. Choi and J.-G. Liu, The reconstruction of upwind fluxes for conservation laws, its behavior in dynamic and steady state calculations, J. Comput. Phys., vol. 144 (1998), pp. 237-256
  55. E. Xu and J.-G. Liu, Pricing of mortgage-backed securities with option-adjusted spread, Managerial Finance, vol. 24 (1998), pp. 94-109
  56. Weinan E and J.-G. Liu, Finite difference schemes for incompressible flows in the impulse-velocity formulation, J. Comput. Phys., vol. 130 (1997), pp. 67-76
  57. G.-Q. Chen and J.-G. Liu, Convergence of difference schemes with high resolutions to conservation laws, Math. Comp., vol. 66 (1997), pp. 1027-1053
  58. Weinan E and J.-G. Liu, Finite difference methods for 3D viscous incompressible flows in the vorticity-vector potential formulation on non-staggered grids, J. Comput. Phys., vol. 138 (1997), pp. 57-82
  59. J.-G. Liu and Z. Xin, Boundary layer behavior in the fluid-dynamic limit for a nonlinear model Boltzmann equation, Arch. Rat. Mech. Anal., vol. 135 (1996), pp. 61-105
  60. J.-G. Liu and Z. Xin, Kinetic and viscous boundary layers for the Broadwell equations, Transport Theory Statist. Phys., vol. 25 (1996), pp. 447-461
  61. C.D. Levermore and J.-G. Liu, Large oscillations arising from a dispersive numerical scheme, Physica D, vol. 99 (1996), pp. 191-216
  62. Weinan E and J.-G. Liu, Projection method II: Godunov-Ryabenki analysis, SIAM J. Numer. Anal., vol. 33 (1996), pp. 1597-1621
  63. Weinan E and J.-G. Liu, Essential compact scheme for unsteady viscous incompressible flows, J. Comput. Phys., vol. 126 (1996), pp. 122-138
  64. Weinan E and J.-G. Liu, Vorticity boundary condition and related issues for finite difference schemes, J. Comput. Phys., vol. 124 (1996), pp. 368-382
  65. S. Jin and J.-G. Liu, The effects of numerical viscosities I: slowly moving shocks, J. Comput. Phys., vol. 126 (1996), pp. 373-389
  66. S. Jin and J.-G. Liu, Oscillations induced by numerical viscosities, Mat. Contemp., vol. 10 (1996), pp. 169-180
  67. J.-G. Liu and Z. Xin, 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
  68. Weinan E and J.-G. Liu, Projection method I: convergence and numerical boundary layers, SIAM J. Numer. Anal., vol. 32 (1995), pp. 1017-1057
  69. S. Jin and J.-G. Liu, Relaxation and diffusion enhanced dispersive waves, Proc. Roy. Soc. Lon. Ser. A, vol. 446 (1994), pp. 555-563
  70. P. Lefloch and J.-G. Liu, Discrete entropy and monotonicity criteria for hyperbolic conservation laws, C.R. Acad. Sci. Paris., vol. 319 (1994), pp. 881-886
  71. J.-G. Liu and Z. Xin, Nonlinear stability of discrete shocks for systems of conservation laws, Arch. Rat. Mech. Anal., vol. 125 (1993), pp. 217-256
  72. J.-G. Liu and Z. Xin, L1-stability of stationary discrete shocks, Math. Comp., vol. 60 (1993), pp. 233-244
  73. B. Engquist and J.-G. Liu, Numerical methods for oscillatory solutions to hyperbolic problems, Comm. Pure Appl. Math., vol. 46 (1993), pp. 1327-1361
  74. G.-Q. Chen and J.-G. Liu, Convergence of second-order schemes for isentropic gas dynamics, Math. Comp., vol. 61 (1993), pp. 607-629

Papers Accepted

  1. J. Haack, S. Jin and J.-G. Liu, An all-speed asymptotic-preserving method for the isentropic Euler and Navier-Stokes equations, Commun. Comput. Phy. (2011)
  2. 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" (2011)
  3. A. Chertock, J.-G. Liu, and T. Pendleton, Convergence of a particle method and global weak solutions of a family of evolutionary PDEs, SIAM Numer. Anal. (2011)
  4. P. Degond and J.-G. Liu, Hydrodynamics of self-alignment interactions with precession and derivation of the Landau-Lifschitz-Gilbert equation, Math. Models Methods Appl. Sci. (2011)
  5. S. Jin, J.-G. Liu and L. Wang, A domain decomposition method for semilinear hyperbolic systems with two-scale relaxations, Math. Comp. (2011)
  6. J. Carrillo, L. Chen, J.-G. Liu and J. Wang, A Note on the Subcritical Two Dimensional Keller-Segel System, Acta Applicanda Mathematicae (2011)
Last modified: 2011/12/12