Weak Solutions of McKean-Vlasov SDEs with Supercritical Drifts  

作　　者：Xicheng Zhang 

机构地区：[1]School of Mathematics and Statistics,Wuhan University,Wuhan,Hubei 430072,People’s Republic of China

出　　处：《Communications in Mathematics and Statistics》2024年第1期1-14,共14页数学与统计通讯（英文）

基　　金：supported by NNSFC Grant of China(No.11731009,12131019);the DFG through the CRC 1283“Taming uncertainty and profiting from randomness and low regularity in analysis,stochastics and their applications”.

摘　　要：Consider the following McKean-Vlasov SDE:dXt=√2dWt+∫R_(d)K(t,Xt-y)μX_(t)(dy)dt,X_(0)=X,whereμXt stands forthedistributionof Xt and K(t,x):R_(+)×R^(d)→is a time-dependent divergence free vector field.Under the assumption K∈L_(x)^(p)with weak solutions to the above SDE.As an application,we provide a new proof for the existence of weak solutions to 2D Navier-Stokes equations with measure as initial vorticity.

关 键 词：McKean-Vlasovsystem Supercritical drift 2D Navier-Stokes equation Krylov’sestimate 

分 类 号：O17[理学—数学]