中科院数学与系统科学研究院

数学研究所

学术报告

调和分析和偏微分方程研讨班

报告人： 朱蓉禅 （北理工）

题  目：Singular SPDEs via convex integration

时  间：2022.06.21（星期二）17:00-18:00

地  点：腾讯会议 151-811-141

摘 要：I will present some applications to singular SPDEs via convex integration. In particular,  we establish 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, solutions are expected to have  space regularity at most $-1/2-\kappa$ for any $\kappa>0$. Consequently, the convective term is  ill-defined analytically and probabilistic renormalization is required. With the help of paracontrolled calculus we decompose  the system in a way which makes it amenable to convex integration.  Finally I will present some open problems in the field of singular SPDEs. Based on joint work with Martina Hofmanova and Xiangchan Zhu.