报 告 人：朱湘禅 研究员

报告题目：Stochastic Navier-Stokes equations via convex integration

报告时间：2023年11月29日（周三）下午16:00-16:50

报告地点：腾讯会议：867-643-3509

主办单位：bat365中文官方网站、数学研究院、科学技术研究院

报告人简介：

       朱湘禅，中科院数学与系统科学研究院研究员，博士生导师。博士毕业于北京大学和德国比勒菲尔德大学，主要从事随机偏微分方程，随机分析和狄氏型理论等相关研究。目前已在Comm. Pure Appl. Math., J. Eur. Math. Soc., Ann. Probab.,  Probab., Theory Related Fields, Arch. Ration. Mech. Anal., Comm. Math. Phys., J. Funct. Anal., Trans. Amer. Math. Soc.等高水平期刊发表论文30余篇。

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. Third we obtain 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.