Math @ Duke

JianGuo Liu, Professor of Physics and Mathematics
 Contact Info:
 Education:
Ph.D.  University of California at Los Angeles  1990 
M.S.  Fudan University (China)  1985 
B.S.  Fudan University (China)  1982 
 Specialties:

Applied Math
 Research Interests: Applied Mathematics, Nonlinear Partial Differential 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
 Keywords:
FokkerPlanck equation • NavierStokes equations
 Curriculum Vitae
 Current Ph.D. Students
(Former Students)
 Representative Publications
(More 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 A, 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. 10171070, 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 [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
 Selected Invited Lectures
 Particle Systems and Partial Differential Equations III, December, 2014, the University of Minho in Braga, Portugal
 A kinetic mean field game theory for the evolution of wealth, May 13, 2014, USA Census Bureau
 An analysis of mergingsplitting group dynamics by Bernstein function theory, April, 2014, ``Modern Perspectives in Applied Mathematics: Theory and Numerics of PDEs'', Maryland
 Phase transition of selfalignment in flocking dynamics, September 07, 2012, "Applied Partial Differential Equations in Physics, Biology and Social Sciences: Classical and Modern Perspectives'', Bellaterra, Spain
 Viscek flocking dynamics and phase transition, June 28, 2012, "14th International Conference on Hyperbolic Problems: Theory, Numerics, Applications'', Università di Padova, Italy
 Selected Invited Lectures
 Phase transitions for selforganized dynamics and sweeping networks, January, 2013, conference on "Transport Models for Collective Dynamics in Biological Systems", NCSU
 Pressure boundary condition and projection method, September, 2011, "Modern Techniques in the Numerical Solution of Partial Differential Equations'', Crete, Greece
 Asymptoticpreserving schemes for some kinetic equations, January, 2011, Workshop on "Numerical Methods for stiff problems in Hamiltonian systems and kinetic equations", SaintMalo, France
 Dynamics of orientational alignment and phase transition, October, 2010, 2010 NIMS Thematic Program Workshop on Conservation Laws, Plasma and Related Fields, Seoul National University, South Korea
 Analysis of Dynamics of DoiOnsager Phase Transition, September 6, 2010, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK
 On incompressible NavierStokes dynamics: a new approach for analysis and computation, May, 2007, The second MINNHOKEE memorial lecturer, Seoul National University
 On incompressible NavierStokes dynamics: a new approach for analysis and computation, September, 2004, Plenary Lecturer, The Tenth International Conference on Hyperbolic Problems: Theory, Numerics and Applications, Osaka, Japan
 Efficient numerical methods for incompressible flows, March, 2002, keynote Speaker, The Tenth South Eastern Approximation Theory Conference, Athens, Georgia
 Recent Grant Support
 Collaborative Research: Kinetic Models of Aggregation and Dispersion, National Science Foundation, 2015/072018/06.
 Conferences Organized
 Organized with Jianfeng Lu a conference Collective Dynamics in Biological and Social Systems, Nov 19  22, 2015
 Coorganized SIAM Conference on Analysis of Partial Differential Equations, minisymposium: Asymptotically Preserving Numerical Methods for TimeDepe, December 2013
 Organizer Committee : IMA Workshop on Analysis and Computation of Incompressible Fluid Flow. February 2010, Organizer Committee : IMA Workshop on Analysis and Computation of Incompressible Fluid Flow, February, 2010
 Organizer Committee, Singapore : Two Month Program on Mathematical Theory and Numerical Methods for Computational Materials Simulation and Design. Jul, Organizer Committee, Singapore : Two Month Program on Mathematical Theory and Numerical Methods for Computational Materials Simulation and Design, July, 2009  August, 2009
 "Twelfth International Conference on Hyperbolic Problems Theory, Numerics, Applications'', Maryland, CoChair, June, 2008
 CSCAMM Workshop on Analytical and Computational Challenges of Incompressible Flows at High Reynolds Number, Organizer Committee, Maryland, October 23, 2006  October 26, 2006
 The Nonlinear Partial Differential Equations: Analysis, Numerics and Applications, Organizing Committee, Singapore, May, 2005
 Two month program on ``Nanoscale Material Interfaces: Experiment, Theory and Simulation'', CoChair, Singapore, November 24, 2004  January 23, 2005
 First Singapore Workshop on PDE and Scientific Computing, CoChair, December, 2004


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

