Abstract for the talk on 02.05.2023 (15:15 h)

OS Analysis-Probability

Martina Hofmanova (Universität Bielefeld)
Non-unique ergodicity for stochastic 3D Navier–Stokes and Euler equations

We establish existence of infinitely many stationary solutions as well as ergodic stationary solutions to the three dimensional Navier–Stokes and Euler equations in the deterministic as well as stochastic setting, driven by an additive noise. The solutions belong to the regularity class \(C(\mathbb{R};H^{\vartheta})\cap C^{\vartheta}(\mathbb{R};L^{2})\) for some \(\vartheta>0\) and satisfy the equations in an analytically weak sense. The result is based on a stochastic variant of the convex integration method which provides uniform moment bounds locally in the aforementioned function spaces.