Global existence for the stochastic Boussinesq equations with transport noise and small rough data

Quyuan Lin; Rongchang Liu; Weinan Wang

Global existence for the stochastic Boussinesq equations with transport noise and small rough data

Analysis of PDEs 2023-03-24 v2

Authors: Quyuan Lin , Rongchang Liu , Weinan Wang

Abstract

In this paper, we consider the stochastic Boussinesq equations on $\mathbb T^3$ with transport noise and rough initial data. We first prove the existence and uniqueness of the local pathwise solution with initial data in $L^p(\Omega;L^p)$ for $p>5$ . By assuming additional smallness on the initial data and the noise, we establish the global existence of the pathwise solution.

Keywords

stochastic boussinesq equations transport noise rough initial data pathwise solution local existence global existence smallness assumption

Cite

@article{arxiv.2303.09768,
  title  = {Global existence for the stochastic Boussinesq equations with transport noise and small rough data},
  author = {Quyuan Lin and Rongchang Liu and Weinan Wang},
  journal= {arXiv preprint arXiv:2303.09768},
  year   = {2023}
}

Comments

24 pages

Related papers

View all related →

Probability · Mathematics

Global existence of the stochastic Navier-Stokes equations in $L^3$ with small data