Nonuniqueness in law of stochastic 3d navierstokes equations with general multiplicative noise

Huaxiang Lv; Yichun Zhu

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arXiv · 2505.07181

Nonuniqueness in law of stochastic 3d navierstokes equations with general multiplicative noise

Huaxiang Lv·Yichun Zhu

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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.

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Huaxiang Lv, Yichun Zhu. 2025-05-12. Nonuniqueness in law of stochastic 3d navierstokes equations with general multiplicative noise. https://arxiv.org/abs/2505.07181

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