Probability Seminar——GLOBAL EXISTENCE AND NON-UNIQUENESS FOR 3D NAVIER–STOKES EQUATIONS WITH SPACE-TIME WHITE NOISE
报告人：Xiangchan Zhu(Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
时间：2022-02-28 14:00-15:00
地点：Room 1114, Sciences Building No. 1
Abstract：
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 − κ for any κ > 0. Consequently, the convective term is ill-defined analytically and probabilistic renormalization is required. Up to now, only local well-posedness has been known. With the help of paracontrolled calculus we decompose the system in a way which makes it amenable to convex integration. By a careful analysis of the regularity of each term, we develop an iterative procedure which yields global non-unique probabilistically strong paracontrolled solutions. Our result applies to any divergence free initial condition in L2 ∪ B −1+κ∞,∞ , κ > 0, and implies also non-uniqueness in law.
