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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. 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 (October, 2014), pp. 1051-1084, ISSN 0003-9527 [doi[abs]
  2. Degond, P; Liu, J-G; Ringhofer, C, Evolution of wealth in a non-conservative economy driven by local Nash equilibria., Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences, vol. 372 no. 2028 (November, 2014), pp. 20130394-20130394, The Royal Society, ISSN 1364-503X [doi[abs]
  3. Bian, S; Liu, JG, Dynamic and Steady States for Multi-Dimensional Keller-Segel Model with Diffusion Exponent m > 0, Communications in Mathematical Physics, vol. 323 no. 3 (November, 2013), pp. 1017-1070, Springer Nature, ISSN 0010-3616 [doi[abs]
  4. Frouvelle, A; Liu, JG, Dynamics in a kinetic model of oriented particles with phase transition, Siam J. Math Anal, vol. 44 no. 2 (2012), pp. 791-826, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1410 [doi[abs]
  5. Ha, SY; Liu, JG, A simple proof of the Cucker-Smale flocking dynamics and mean-field limit, Commun. Math. Sci., vol. 7 no. 2 (2009), pp. 297-325, International Press of Boston, ISSN 1539-6746 [doi[abs]
  6. Liu, JG; 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
  7. Johnston, H; Liu, JG, Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term, Journal of Computational Physics, vol. 199 no. 1 (September, 2004), pp. 221-259, Elsevier BV [doi[abs]
  8. Weinan, E; Liu, JG, Vorticity boundary condition and related issues for finite difference schemes, Journal of Computational Physics, vol. 124 no. 2 (March, 1996), pp. 368-382, Elsevier BV [doi[abs]
  9. Liu, JG; 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 no. 6 (1995), pp. 611-628 [doi[abs]
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Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320