学术报告（洪伟 10.28）

 摘要 In this talk, we review the recent results on the McKean-Vlasov stochastic (partial) differential equations. The existence and uniqueness results state that we only need to impose some local assumptions on the coefficients, i.e. locally monotone condition both in state variable and distribution variable, which cause some essential difficulty since the coefficients of McKean-Vlasov stochastic equations typically are nonlocal. Furthermore, we show a propagation of chaos result in Wasserstein distance for weakly interacting stochastic 2D Navier-Stokes systems with the interaction term being e.g. {\it{Stokes drag force}} that is proportional to the relative velocity of the particles. Finally, we also introduce some recent works on the multi-scale McKean-Vlasov stochastic dynamical system, including averaging principle, normal deviations, large deviation principle and moderate deviation principle.