# Jian-Guo Liu

### **Professor of Physics**

Professor of Mathematics (Joint)

Professor of Mathematics and Physics at Duke Kunshan University

Professor of Mathematics (Joint)

Professor of Mathematics and Physics at Duke Kunshan University

### 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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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## 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.
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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.
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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.