**Keywords:**- Fokker-Planck equation, Navier-Stokes 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

**Representative 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] - 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] - 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] - 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] - 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,