Jian-Guo Liu, Professor of Physics and Mathematics

Jian-Guo Liu
Office Location:  285 Physics Bldg, Durham, NC 27708
Office Phone:  (919) 660-2500
Email Address: send me a message
Web Page:  http://www.math.duke.edu/~jliu/

Teaching (Fall 2017):

Education:

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

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

Keywords:

Fokker-Planck equation • Navier-Stokes equations

Current Ph.D. Students  

Representative Publications

  1. 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, ISSN 0003-9527 [doi]  [abs]
  2. 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]
  3. 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, ISSN 1364-503X [doi]
  4. 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, ISSN 0010-3616 [doi]  [abs]
  5. 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, ISSN 0036-1410 [doi]  [abs]
  6. 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, ISSN 1539-6746  [abs]
  7. 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
  8. 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 [doi]  [abs]
  9. 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 [doi]  [abs]
  10. 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
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'', Universit√† 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