Jian-Guo Liu

Jian-Guo Liu

Professor of Physics

Professor of Mathematics (Joint)

Professor of Mathematics and Physics at Duke Kunshan University

Office Location: 
285 Physics Bldg, Durham, NC 27708
Front Office Address: 
Box 90320, Durham, NC 27708-0320
Phone: 
(919) 660-2500

Selected Grants

Collaborative Research: Nonlocal models of aggregation and dispersion awarded by National Science Foundation (Principal Investigator). 2018 to 2021

Collaborative Research: Kinetic Models of Aggregation and Dispersion awarded by National Science Foundation (Principal Investigator). 2015 to 2019

Efficient Numerical Methods for Viscous Incompressible Flows awarded by National Science Foundation (Principal Investigator). 2009 to 2012

Gao, Y., et al. “Analysis of a continuum theory for broken bond crystal surface models with evaporation and deposition effects.” Nonlinearity, vol. 33, no. 8, Aug. 2020, pp. 3816–45. Scopus, doi:10.1088/1361-6544/ab853d. Full Text

Li, Lei, and Jian-Guo Liu. “Large time behaviors of upwind schemes and $B$-schemes for Fokker-Planck equations on $\mathbb {R}$ by jump processes.” Mathematics of Computation, vol. 89, no. 325, American Mathematical Society (AMS), Feb. 2020, pp. 2283–320. Crossref, doi:10.1090/mcom/3516. Full Text

Degond, P., et al. “A markov jump process modelling animal group size statistics.” Communications in Mathematical Sciences, vol. 18, no. 1, Jan. 2020, pp. 55–89. Scopus, doi:10.4310/CMS.2020.v18.n1.a3. Full Text

Li, L., et al. “A stochastic version of stein variational gradient descent for efficient sampling.” Communications in Applied Mathematics and Computational Science, vol. 15, no. 1, Jan. 2020, pp. 37–63. Scopus, doi:10.2140/camcos.2020.15.37. Full Text Open Access Copy

Jin, S., et al. “Random Batch Methods (RBM) for interacting particle systems.” Journal of Computational Physics, vol. 400, Jan. 2020. Scopus, doi:10.1016/j.jcp.2019.108877. Full Text

Feng, Y., et al. “Uniform-in-time weak error analysis for stochastic gradient descent algorithms via diffusion approximation.” Communications in Mathematical Sciences, vol. 18, no. 1, Jan. 2020, pp. 163–88. Scopus, doi:10.4310/CMS.2020.v18.n1.a7. Full Text

Li, L., et al. “On the mean field limit for Brownian particles with Coulomb interaction in 3D.” Journal of Mathematical Physics, vol. 60, no. 11, Nov. 2019. Scopus, doi:10.1063/1.5114854. Full Text

Liu, J. G., and R. L. Pego. “On Local Singularities in Ideal Potential Flows with Free Surface.” Chinese Annals of Mathematics. Series B, vol. 40, no. 6, Nov. 2019, pp. 925–48. Scopus, doi:10.1007/s11401-019-0167-z. Full Text

Liu, J. G., et al. “Well-posedness and derivative blow-up for a dispersionless regularized shallow water system.” Nonlinearity, vol. 32, no. 11, Oct. 2019, pp. 4346–76. Scopus, doi:10.1088/1361-6544/ab2cf1. Full Text

Liu, J. G., et al. “Least action principles for incompressible flows and geodesics between shapes.” Calculus of Variations and Partial Differential Equations, vol. 58, no. 5, Oct. 2019. Scopus, doi:10.1007/s00526-019-1636-7. Full Text

Pages

Frouvelle, A., and J. G. Liu. “Long-Time Dynamics for a Simple Aggregation Equation on the Sphere.” Springer Proceedings in Mathematics and Statistics, vol. 282, 2019, pp. 457–79. Scopus, doi:10.1007/978-3-030-15096-9_16. Full Text

Liu, J. G., and Y. Zhang. “Convergence of diffusion-drift many particle systems in probability under a sobolev norm.” Springer Proceedings in Mathematics and Statistics, vol. 162, 2016, pp. 195–223. Scopus, doi:10.1007/978-3-319-32144-8_10. Full Text

Degond, Pierre, et al. “A NOTE ON PHASE TRANSITIONS FOR THE SMOLUCHOWSKI EQUATION WITH DIPOLAR POTENTIAL.” Hyperbolic Problems: Theory, Numerics, Applications, edited by F. Ancona et al., vol. 8, AMER INST MATHEMATICAL SCIENCES-AIMS, 2014, pp. 179–92.