Math @ Duke

Research Interests for JianGuo Liu
Research Interests: Applied Mathematics, Nonlinear Partial Differential Equations.
 Keywords:
 FokkerPlanck equation, NavierStokes equations
 Areas of Interest:
Collective dynamics, decision making and selforganization 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 SelfOrganized Alignment Dynamics,
Archive for Rational Mechanics and Analysis, vol. 216 no. 1
(January, 2015),
pp. 63115, ISSN 00039527 [doi] [abs]
 Coquel, F; Jin, S; Liu, JG; Wang, L, WellPosedness and Singular Limit of a Semilinear Hyperbolic Relaxation System with a TwoScale Discontinuous Relaxation Rate,
Archive for Rational Mechanics and Analysis, vol. 214 no. 3
(January, 2014),
pp. 10511084, ISSN 00039527 [doi] [abs]
 Degond, P; Liu, JG; Ringhofer, C, Evolution of wealth in a nonconservative economy driven by local Nash equilibria,
Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences, vol. 372 no. 2028
(October, 2014),
pp. 2013039420130394, ISSN 1364503X [doi]
 Bian, S; Liu, JG, Dynamic and Steady States for MultiDimensional KellerSegel Model with Diffusion Exponent m > 0,
Communications in Mathematical Physics, vol. 323 no. 3
(2013),
pp. 154, ISSN 00103616 [doi] [abs]
 Frouvelle, A; Liu, JG, Dynamics in a kinetic model of oriented particles with phase transition,
Siam Journal on Mathematical Analysis, vol. 44 no. 2
(2012),
pp. 791826, ISSN 00361410 [doi] [abs]
 Ha, SY; Liu, JG, A simple proof of the CuckerSmale flocking dynamics and meanfield limit,
Communications in Mathematical Sciences, vol. 7 no. 2
(2009),
pp. 297325, ISSN 15396746 [doi] [abs]
 Liu, JG; Liu, J; Pego, R, Stability and convergence of efficient NavierStokes solvers via a commutator estimate via a commutator estimate,
Comm. Pure Appl. Math., vol. 60
(2007),
pp. 14431487
 Johnston, H; Liu, JG, Accurate, stable and efficient NavierStokes solvers based on explicit treatment of the pressure term,
Journal of Computational Physics, vol. 199 no. 1
(2004),
pp. 221259 [doi] [abs]
 Weinan, E; Liu, JG, Vorticity boundary condition and related issues for finite difference schemes,
Journal of Computational Physics, vol. 124 no. 2
(1996),
pp. 368382 [doi] [abs]
 Liu, JG; Xin, Z, Convergence of vortex methods for weak solutions to the 2D Euler equations with vortex sheets data,
Comm. Pure Appl. Math., vol. 48
(1995),
pp. 611628


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