報 告 人：朱湘禪 研究員

報告題目：Stochastic Navier-Stokes equations via convex integration

報告時間：2023年11月29日（周三）下午16:00-16:50

報告地點：騰訊會議：867-643-3509

主辦單位：數學與統計學院、數學研究院、科學技術研究院

報告人簡介：

       朱湘禪，中科院數學與系統科學研究院研究員，博士生導師。博士畢業于北京大學和德國比勒菲爾德大學，主要從事隨機偏微分方程，隨機分析和狄氏型理論等相關研究。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.等高水平期刊發表論文30余篇。

報告摘要：

       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.