English

Almost global existence for the stochastic Navier-Stokes equations with small $H^{1/2}$ data

Probability 2025-01-20 v1 Analysis of PDEs

Abstract

We address the global existence of solutions to the stochastic Navier-Stokes equations with multiplicative noise and with initial data in H1/2(T3)H^{1/2}(\mathbb{T}^{3}). We prove that the solution exists globally in time with probability arbitrarily close to~11 if the initial data and noise are sufficiently small. If the noise is not assumed to be small, then the solution is global on a sufficiently small deterministic time interval with probability arbitrarily close to~11.

Keywords

Cite

@article{arxiv.2501.10331,
  title  = {Almost global existence for the stochastic Navier-Stokes equations with small $H^{1/2}$ data},
  author = {Mustafa Sencer Aydın and Igor Kukavica and Fanhui Xu},
  journal= {arXiv preprint arXiv:2501.10331},
  year   = {2025}
}
R2 v1 2026-06-28T21:09:33.002Z