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Jian-Guo Liu, Professor

Jian-Guo Liu
Contact Info:
Office Location:  285 Physics
Office Phone:  919-660-2546
Email Address: send me a message
Web Page:

Teaching (Fall 2014):

  • MATH 651.01, HYPERBOLIC PDE Synopsis
    SEE INSTRU, TuTh 03:05 PM-04:20 PM
    Physics 299, TuTh 01:25 PM-02:40 PM
Teaching (Spring 2015):

    Physics 259, TuTh 03:05 PM-04:20 PM

PhDUniversity of California, Los Angeles1990
MSFudan University1985
BSFudan University1982

Applied Math
Research Interests: Applied Mathematics, Nonlinear Partial Differential Equations.

Areas of Interest:

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

Curriculum Vitae
Current Ph.D. Students   (Former Students)

    Representative Publications   (More Publications)

    1. P. Degond, J.-G. Liu and C. Ringhofer, Evolution of the distribution of wealth in an economic environment driven by local Nash equilibria, J. Stat. Phys. (Accepted, 2013)
    2. S. Bian and J.-G. Liu, Dynamic and steady states for multi-dimensional Keller-Segel model with diffusion exponent m > 0, Comm Math Phy, vol. 323 (2013), pp. 1017-1070
    3. A. Frouvelle and J.-G. Liu, Dynamics in a kinetic model of oriented particles with phase transition, SIAM J. Math Anal, vol. 44 (2012), pp. 791--826
    4. 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
    5. 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
    6. 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
    7. 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
    8. Weinan E and J.-G. Liu, Gauge method for viscous incompressible flows, Comm. Math. Sci., vol. 1 (2003), pp. 317--332
    9. 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
    10. 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
    Selected Invited Lectures

    1. Viscek flocking dynamics and phase transition, June 28, 2012, ``14th International Conference on Hyperbolic Problems: Theory, Numerics, Applications'', Universit√† di Padova, Italy    
    2. Phase transition of self-alignment in flocking dynamics, September 07, 2012, ``Applied Partial Differential Equations in Physics, Biology and Social Sciences: Classical and Modern Perspectives'', Bellaterra, Spain    
    3. Mathematical analysis of flocking dynamics in biology and social science, June 19, 2012, USA Census Bureau    
    Selected Invited Lectures

    1. Pressure boundary condition and projection method, September, 2011, ``Modern Techniques in the Numerical Solution of Partial Differential Equations'', Crete, Greece    
    2. Asymptotic-preserving schemes for some kinetic equations, January, 2011, Workshop on "Numerical Methods for stiff problems in Hamiltonian systems and kinetic equations", Saint-Malo, France    
    3. Dynamics of orientational alignment and phase transition, October, 2010, 2010 NIMS Thematic Program Workshop on Conservation Laws, Plasma and Related Fields, Seoul National University, South Korea    
    4. Analysis of Dynamics of Doi-Onsager Phase Transition, September 6, 2010, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK    
    5. A simple proof of the Cucker-Smale flocking dynamics and mean-field limit, July, 2009, ICMS Workshop on Kinetic and Mean-field models in the Socio-Economic Sciences, Edinburgh, UK,    
    6. A simple proof of the Cucker-Smale flocking dynamics and mean-field limit, July, 2009, Workshop on Kinetics and statistical methods for complex particle systems, Lisbon, Portugal    
    7. On incompressible Navier-Stokes dynamics: a new approach for analysis and computation, May, 2007, The second MINNHOKEE memorial lecturer, Seoul National University    
    8. On incompressible Navier-Stokes dynamics: a new approach for analysis and computation, September, 2004, Plenary Lecturer, The Tenth International Conference on Hyperbolic Problems: Theory, Numerics and Applications, Osaka, Japan    
    9. Efficient numerical methods for incompressible flows, March, 2002, keynote Speaker, The Tenth South Eastern Approximation Theory Conference, Athens, Georgia    
    Recent Grant Support

    • Efficient Numerical Methods for Viscous Incompressible Flows, National Science Foundation, 1011738, 2009/07-2012/06.      
    Conferences Organized

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

    ph: 919.660.2800
    fax: 919.660.2821

    Mathematics Department
    Duke University, Box 90320
    Durham, NC 27708-0320