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arXiv · 2303.09768

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

Quyuan Lin·Rongchang Liu·Weinan Wang
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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.

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Quyuan Lin, Rongchang Liu, Weinan Wang. 2023-03-17. Global existence for the stochastic Boussinesq equations with transport noise and small rough data. https://arxiv.org/abs/2303.09768

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