Jian-Guo Liu, Professor of Physics and Mathematics and Professor of Mathematics and Physics at Duke Kunshan University

Jian-Guo Liu
Office Location:  285 Physics Bldg, Durham, NC 27708
Office Phone:  (919) 660-2546
Email Address: send me a message
Web Page:  http://www.math.duke.edu/~jliu/


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

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


Fokker-Planck equation • Navier-Stokes equations

Current Ph.D. Students  

Representative Publications

  1. 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, ISSN 0003-9527 [doi]  [abs]
  2. Degond, P; Liu, J-G; Ringhofer, C, Evolution of wealth in a non-conservative economy driven by local Nash equilibria., Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences, vol. 372 no. 2028 (November, 2014), pp. 20130394-20130394, The Royal Society, ISSN 1364-503X [doi]  [abs]
  3. Bian, S; Liu, JG, Dynamic and Steady States for Multi-Dimensional Keller-Segel Model with Diffusion Exponent m > 0, Communications in Mathematical Physics, vol. 323 no. 3 (November, 2013), pp. 1017-1070, Springer Nature, ISSN 0010-3616 [doi]  [abs]
  4. Frouvelle, A; Liu, JG, Dynamics in a kinetic model of oriented particles with phase transition, Siam J. Math Anal, vol. 44 no. 2 (2012), pp. 791-826, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1410 [doi]  [abs]
  5. Ha, SY; Liu, JG, A simple proof of the Cucker-Smale flocking dynamics and mean-field limit, Commun. Math. Sci., vol. 7 no. 2 (2009), pp. 297-325, International Press of Boston, ISSN 1539-6746 [doi]  [abs]
  6. Liu, JG; Liu, J; Pego, R, Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate via a commutator estimate, Comm. Pure Appl. Math., vol. 60 (2007), pp. 1443-1487
  7. Johnston, H; Liu, JG, Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term, Journal of Computational Physics, vol. 199 no. 1 (September, 2004), pp. 221-259, Elsevier BV [doi]  [abs]
  8. Weinan, E; Liu, JG, Vorticity boundary condition and related issues for finite difference schemes, Journal of Computational Physics, vol. 124 no. 2 (March, 1996), pp. 368-382, Elsevier BV [doi]  [abs]
  9. Liu, J; Xin, Z, Convergence of vortex methods for weak solutions to the 2‐D euler equations with vortex sheet data, Communications on Pure and Applied Mathematics, vol. 48 no. 6 (January, 1995), pp. 611-628 [doi]  [abs]
Selected Invited Lectures

  1. Particle Systems and Partial Differential Equations III, December, 2014, the University of Minho in Braga, Portugal    
  2. A kinetic mean field game theory for the evolution of wealth, May 13, 2014, USA Census Bureau    
  3. An analysis of merging-splitting group dynamics by Bernstein function theory, April, 2014, ``Modern Perspectives in Applied Mathematics: Theory and Numerics of PDEs'', Maryland    
  4. 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    
  5. Viscek flocking dynamics and phase transition, June 28, 2012, "14th International Conference on Hyperbolic Problems: Theory, Numerics, Applications'', Università di Padova, Italy    
Selected Invited Lectures

  1. Phase transitions for self-organized dynamics and sweeping networks, January, 2013, conference on "Transport Models for Collective Dynamics in Biological Systems", NCSU    
  2. Pressure boundary condition and projection method, September, 2011, "Modern Techniques in the Numerical Solution of Partial Differential Equations'', Crete, Greece    
  3. 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    
  4. 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    
  5. Analysis of Dynamics of Doi-Onsager Phase Transition, September 6, 2010, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK    
  6. On incompressible Navier-Stokes dynamics: a new approach for analysis and computation, May, 2007, The second MINNHOKEE memorial lecturer, Seoul National University    
  7. 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    
  8. Efficient numerical methods for incompressible flows, March, 2002, keynote Speaker, The Tenth South Eastern Approximation Theory Conference, Athens, Georgia    
Recent Grant Support

Conferences Organized