報(bào) 告 人：朱湘禪 研究員

報(bào)告題目：Stochastic Navier-Stokes equations via convex integration

報(bào)告時(shí)間：2023年11月29日（周三）下午16:00-16:50

報(bào)告地點(diǎn)：騰訊會(huì)議：867-643-3509

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報(bào)告人簡(jiǎn)介：

       朱湘禪，中科院數(shù)學(xué)與系統(tǒng)科學(xué)研究院研究員，博士生導(dǎo)師。博士畢業(yè)于北京大學(xué)和德國(guó)比勒菲爾德大學(xué)，主要從事隨機(jī)偏微分方程，隨機(jī)分析和狄氏型理論等相關(guān)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(fā)表論文30余篇。

報(bào)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.