Stochastic Navier-Stokes equations on a thin spherical domain

Abstract

Incompressible Navier-Stokes equations on a thin spherical domain $Q_{\epsilon }$ along with free boundary conditions under a random forcing are considered. The convergence of the martingale solution of these equations to the martingale solution of the stochastic Navier-Stokes equations on a sphere ${\mathbb{S}}^2$ as the thickness converges to zero is established.

54 Pages. Published Version. Includes additional sections corresponding to the analysis of deterministic NSEs on a thin spherical domain