English

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}
}