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

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.

46 pages. Dedicated to the memory of Igor D. Chueshov

References in corpus (2)

• Global L_2-solutions of stochastic Navier-Stokes equations
• Well-Posedness of the 3D Stochastic Primitive Equations with Transport Noise