Math @ Duke

JianGuo Liu, Professor
 Contact Info:
Teaching (Fall 2014):
 MATH 651.01, HYPERBOLIC PDE
Synopsis
 SEE INSTRU, TuTh 03:05 PM04:20 PM
 PHYSICS 763.01, STATISTICAL MECHANICS
Synopsis
 Physics 299, TuTh 01:25 PM02:40 PM
 Education:
PhD  University of California, Los Angeles  1990 
MS  Fudan University  1985 
BS  Fudan University  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
 Curriculum Vitae
 Current Ph.D. Students
(Former Students)
 Representative Publications
(More Publications)
 P. Degond, J.G. Liu and C. Ringhofer, Evolution of the distribution of wealth in an economic environment driven by local Nash equilibria,
J. Stat. Phys.
(Accepted, 2013)
 S. Bian and J.G. Liu, Dynamic and steady states for multidimensional KellerSegel model with diffusion exponent m > 0,
Comm Math Phy, vol. 323
(2013),
pp. 10171070
 A. Frouvelle and J.G. Liu, Dynamics in a kinetic model of oriented particles with phase transition,
SIAM J. Math Anal, vol. 44
(2012),
pp. 791826
 S.Y. Ha and J.G. Liu, A simple proof of the CuckerSmale flocking dynamics and meanfield limit,
Commun. Math. Sci., vol. 7
(2009),
pp. 297325
 J.G. Liu, J. Liu and R. Pego, Stability and convergence of efficient NavierStokes solvers via a commutator estimate via a commutator estimate,
Comm. Pure Appl. Math., vol. 60
(2007),
pp. 14431487
 H. Johnston and J.G. Liu, Accurate, stable and efficient NavierStokes solvers based on explicit treatment of the pressure term,
J. Comput. Phys., vol. 188
(2004),
pp. 221259
 J.G. Liu and W.C. Wang, Energy and helicity preserving schemes for hydro and magnetohydrodynamics flows with symmetry,
J. Comput. Phys., vol. 200
(2004),
pp. 833
 Weinan E and J.G. Liu, Gauge method for viscous incompressible flows,
Comm. Math. Sci., vol. 1
(2003),
pp. 317332
 Weinan E and J.G. Liu, Vorticity boundary condition and related issues for finite difference schemes,
J. Comput. Phys., vol. 124
(1996),
pp. 368382
 J.G. Liu and Z. Xin, 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
 Viscek flocking dynamics and phase transition, June 28, 2012, ``14th International Conference on Hyperbolic Problems: Theory, Numerics, Applications'', Università di Padova, Italy
 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
 Mathematical analysis of flocking dynamics in biology and social science, June 19, 2012, USA Census Bureau
 Selected Invited Lectures
 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
 A simple proof of the CuckerSmale flocking dynamics and meanfield limit, July, 2009, ICMS Workshop on Kinetic and Meanfield models in the SocioEconomic Sciences, Edinburgh, UK,
 A simple proof of the CuckerSmale flocking dynamics and meanfield limit, July, 2009, Workshop on Kinetics and statistical methods for complex particle systems, Lisbon, Portugal
 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
 Efficient Numerical Methods for Viscous Incompressible Flows, National Science Foundation, 1011738, 2009/072012/06.
 Conferences Organized
 Coorganized SIAM Conference on Analysis of Partial Differential Equations, minisymposium: Asymptotically Preserving Numerical Methods for TimeDepe, December 2013
 IMA Workshop on Analysis and Computation of Incompressible Fluid Flow, Organizer Committee, February, 2010
 Two Month Program on Mathematical Theory and Numerical Methods for Computational Materials Simulation and Design, Organizer Committee, Singapore, 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

