**Office Location:** 285 Physics**Office Phone:** 919-660-2546**Email Address:** jian-guo.liu@duke.edu**Web Page:** http://www.math.duke.edu/~jliu/

**Specialties:**

Nonlinear dynamics and complex systems

Biological physics

**Education:**

PhD, University of California, Los Angeles, 1990

MS, Fudan University, 1985

BS, Fudan University, 1982

**Research Categories:** *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

**Teaching (Fall 2014):**

- Math 651.01,
*Hyperbolic pde*Synopsis- See instru, TuTh 03:05 PM-04:20 PM

- Physics 763.01,
*Statistical mechanics*Synopsis- Physics 299, TuTh 01:25 PM-02:40 PM

**Representative Publications**
(More Publications)

- P. Degond, J.-G. Liu and C. Ringhofer,
*Large-scale dynamics of Mean-Field Games driven by local Nash equilibria*, J Nonlinear Sci. (Accepted, 2013) . - 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) . - 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 . - 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 . - 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 . - 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 . - 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 . - 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 . - 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 . - 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 .

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

**Selected Invited Lectures***Viscek flocking dynamics and phase transition*, June 28, 2012, ``14th International Conference on Hyperbolic Problems: Theory, Numerics, Applications'', Università di Padova, Italy*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*Mathematical analysis of flocking dynamics in biology and social science*, June 19, 2012, USA Census Bureau

**Selected Invited Lectures***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, July, 2009, ICMS Workshop on Kinetic and Mean-field models in the Socio-Economic Sciences, Edinburgh, UK,*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*A simple proof of the Cucker-Smale flocking dynamics and mean-field limit*, 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