Stochastic 2D Navier-Stokes equations on time-dependent domains

2021/05/28 by Wei Wang, Wang, Wei, Jianliang Zhai +3
Computer Science · Economics, Econometrics and Finance · Engineering · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2105.13565

openalex publication_date 2021/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish the existence and uniqueness of solutions to stochastic 2D Navier-Stokes equations in a time-dependent domain driven by Brownian motion. A martingale solution is constructed through domain transformation and appropriate Galerkin approximations on time-dependent spaces. The probabilistic strong solution follows from the pathwise uniqueness and the Yamada-Watanable theorem.

Citations

• Sur le mouvement d'un liquide visqueux emplissant l'espace

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