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### Jian-Guo Liu, Professor of Physics and Mathematics

Office Location: | 285 Physics Bldg, Durham, NC 27708 |

Office Phone: | (919) 660-2500 |

Email Address: | |

Web Page: | http://www.math.duke.edu/~jliu/ |

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

**Specialties:**-
Nonlinear dynamics and complex systems

Applied Math

Biological physics

**Research Interests:***Applied mathematics, nonlinear dynamics, complex system, fluid dynamics, computational sciences*

**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,

Phase transition in non-equilibrium complex systems

Computational fluid dynamics

**Keywords:**Fokker-Planck equation • Navier-Stokes equations

**Current Ph.D. Students**(Former Students)

**Representative Publications**(More Publications)- 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] - 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] - 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] - 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] - 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] - 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, ISSN 0021-9991 [doi] [abs] - 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] - 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 - 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] - 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] - 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

- Degond, P; Frouvelle, A; Liu, JG,

**Selected Invited Lectures***Particle Systems and Partial Differential Equations III*, December, 2014, the University of Minho in Braga, Portugal*A kinetic mean field game theory for the evolution of wealth*, May 13, 2014, USA Census Bureau*An analysis of merging-splitting group dynamics by Bernstein function theory*, April, 2014, ``Modern Perspectives in Applied Mathematics: Theory and Numerics of PDEs'', Maryland*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*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***Phase transitions for self-organized dynamics and sweeping networks*, January, 2013, conference on "Transport Models for Collective Dynamics in Biological Systems", NCSU*Pressure boundary condition and projection method*, September, 2011, "Modern Techniques in the Numerical Solution of Partial Differential Equations'', Crete, Greece*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*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*Analysis of Dynamics of Doi-Onsager Phase Transition*, September 6, 2010, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, May, 2007,*On incompressible Navier-Stokes dynamics: a new approach for analysis and computation***The second MINNHOKEE memorial lecturer,**Seoul National University*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*Efficient numerical methods for incompressible flows*, March, 2002,**keynote Speaker,**The Tenth South Eastern Approximation Theory Conference, Athens, Georgia