Research Interests for Jian-Guo Liu

Research Interests: Applied Mathematics, Nonlinear Partial Differential Equations.

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
  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