Nonuniqueness in law of stochastic 3d navierstokes equations with general multiplicative noise
Probability
2025-05-13 v1
Abstract
We are concerned with the three dimensional navier-stokes equations driven by a general multiplicative noise. For every divergence free and mean free initial condition in L2, we establish existence of infinitely many global-in-time probabilistically strong and analytically weak solutions, which implies non-uniqueness in law. Moreover, we prove the existence of infinitely many ergodic stationary solutions. Our results are based on a stochastic version of the convex integration and the Ito calculus.
Keywords
Cite
@article{arxiv.2505.07181,
title = {Nonuniqueness in law of stochastic 3d navierstokes equations with general multiplicative noise},
author = {Huaxiang Lv and Yichun Zhu},
journal= {arXiv preprint arXiv:2505.07181},
year = {2025}
}