Stochastic Navier--Stokes equations on a 3D thin domain

2020/08/17 by Zdzisław Brzeźniak, Brzeźniak, Zdzisław, Gaurav Dhariwal +3
Computer Science · Mathematics · #35Q30 #76D05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Numerical methods in inverse problems #Primary 60H15 #Probability (math.PR) #Secondary 35R60

paper · pdf · doi:10.48550/arxiv.2008.07394

openalex publication_date 2020/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Stochastic Navier--Stokes equations in a thin three-dimensional domain are considered, driven by additive noise. The convergence of martingale solution of the stochastic Navier--Stokes equations in a thin three-dimensional domain to the unique martingale solution of the 2D stochastic Navier--Stokes equations, as the thickness of the film vanishes, is established. Hence, we justify the approximation of 3D Navier--Stokes equations driven by random forcing by its corresponding two-dimensional setting in applications.

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