Math @ Duke
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Research Interests for Jian-Guo Liu
Research Interests: Applied Mathematics, Nonlinear Partial Differential Equations.
- 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
- 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]
- 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, The Royal Society, ISSN 1364-503X [doi] [abs]
- 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]
- 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]
- 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]
- 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
- 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]
- 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]
- 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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