Topics in Analysis of Many Particle Systems

主讲人:王振富(宾夕法尼亚大学)
时间: 周一,三 9:00-10:30,2020-8-17 ~ 9-2
地点:线上

摘要

Zoom Meeting ID: 290 252 4491 Passcode: 170820

报告人简介

Abstract: This summer course will present some mathematical tools and concepts for the rigorous derivation and study of nonlinear partial differential equations (PDE's) arising from many-particle limits: (McKean-)Vlasov type equations, the vorticity formulation of the 2D incompressible Euler/Navier-Stokes equations, Boltzmann collision equations, nonlinear diffusion equations, quantum Hartree equations... Depending on time and interest it will include part or all of the following topics: the Liouville/Master equations of N-particle systems, the notion of empirical measures, the BBGKY hierarchy,the Hewitt-Savage theorem, the Dobrushin's stability estimate, the coupling method, the concepts of chaos and entropic chaos, the recent progresses on the mean-_eld limit, in particular, the relative entropy/modulated potential energy/modulated free energy methods as introduced in:
This summer course will present some mathematical tools and concepts for the rigorous derivation and study of nonlinear partial differential equations (PDE's) arising from many-particle limits: (McKean-)Vlasov type equations, the vorticity formulation of the 2D incompressible Euler/Navier-Stokes equations, Boltzmann collision equations, nonlinear diffusion equations, quantum Hartree equations... Depending on time and interest it will include part or all of the following topics: the Liouville/Master equations of N-particle systems, the notion of empirical measures, the BBGKY hierarchy,the Hewitt-Savage theorem, the Dobrushin's stability estimate, the coupling method, the concepts of chaos and entropic chaos, the recent progresses on the mean-_eld limit, in particular, the relative entropy/modulated potential energy/modulated free energy methods as introduced in:

——P.-E. Jabin and Z. Wang, Mean Field Limit and Propagation of Chaos for Vlasov Systems with Bounded Forces. J. Funct. Anal. 271 (2016) 3588-3627.

——P.-E. Jabin and Z. Wang, Quantitative estimates of propagation of chaos for stochastic systems with W-1,∞ kernels. Inventiones mathematicae 214(1) (2018) 523-591.

——S. Serfaty (appendix with M. Duerinckx), Mean Field Limit for Coulomb-Type Flows. To appear in Duke Math. J.

——D. Bresch, P.-E. Jabin and Z. Wang. On mean-field limits and quantitative estimates with a large class of singular kernels: Application to the Patlak-Keller-Segel model. Comptes Rendus Mathematique 357(9) (2019) 708-720.

Detailed Abstract Download:/uploads/file/2020/20200701/20200701145751_45224.pdf



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