Wednesday, February 2, 2022 - 14:00 in ZOOM - Video Conference
Global existence and non-uniqueness for 3D Navier--Stokes equations with space-time white noise
A talk in the Bielefeld Stochastic Afternoon series by
Rongchan Zhu
| 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 $-1/2-\kappa$ for any $\kappa>0$. 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 that 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 $L^{2}\cup B^{-1+\kappa}_{\infty,\infty}$, $\kappa>0$, and implies also non-uniqueness in law.
This talk is based on joint work with Martina Hofmanova and Xiangchan Zhu.
Within the CRC this talk is associated to the project(s): B1 |
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