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.
