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Stochastic Navier-Stokes equations via convex integration

发布时间:2022-11-04 浏览量:72

时   间:  2022-11-04 14:00 — 15:00

地   点:  腾讯会议 APP()
报告人:  朱湘禅
单   位:  中科院数学与系统科学研究院应用所
邀请人:  张登
备   注:  腾讯会议:801-128-324,会议密码:123456。报告人简介:朱湘禅,中科院数学与系统科学研究院应用所研究员,2012年于北京大学和德国比勒菲尔德大学获得博士学位。主要研究方向是随机分析和随机偏微分方程,具体包括奇异随机偏微分方程和随机流体方程等。
报告摘要:  

In this talk I will talk about our recent work on the three dimensional stochastic Navier-Stokes equations via convex integration method. First  we establish non-uniqueness in law, existence and non-uniqueness of probabilistically strong solutions and non-uniqueness of the associated Markov processes. Second we prove existence of infinitely many stationary solutions as well as ergodic stationary solutions to the stochastic Navier-Stokes and Euler equations. Moreover, we are able to make conclusions regarding the vanishing viscosity limit and the anomalous dissipation. Finally I will show global-in-time existence and non-uniqueness of probabilistically strong solutions to the three dimensional Navier--Stokes system driven by space-time white noise. In this setting,  the convective term is  ill-defined in the classical sense and probabilistic renormalization is required.