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

2023/03/17 by Quyuan Lin, Lin, Quyuan, Rongchang Liu +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2303.09768

openalex publication_date 2023/03/17 · openalex created_date 2023/03/21 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the stochastic Boussinesq equations on \mathbb T³ 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(Ω;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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• A mixed finite element method for the stochastic Boussinesq equations with multiplicative noise

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