一、报告题目

Global-in-time probabilistically strong and Markov solutions to stochastic 3D Navier--Stokes equations: existence and non-uniqueness

二、主讲人

朱蓉禅

三、报告时间

2021年9月22日 19:00

四、报告地点

腾讯会议 ID : 488 2330 4823

五、摘要

We are concerned with the three dimensional incompressible Navier--Stokes equations driven by an additive stochastic forcing. First, for every divergence free initial condition in $L^{2}$ we establish existence of infinitely many global-in-time probabilistically strong and analytically weak solutions, solving one of the open problems in the field. This result in particular implies non-uniqueness in law. Second,we prove non-uniqueness of the associated Markov processes in a suitably chosen class of analytically weak solutions satisfying a relaxed form of an energy inequality. Translated to the deterministic setting, we obtain non-uniqueness of the associated semiflows.

六、主讲人简介

朱蓉禅，博士毕业于中科院数学与系统科学研究院和德国比勒菲尔德大学，现任北京理工大学教授。2019年获批国家自然科学基金优青项目。

七、主办单位

非线性期望前沿科学中心

数学与交叉科学研究中心