Inviscid limit for Stochastic Navier-Stokes Equations under general initial conditions

TL;DR

This paper proves that solutions of stochastic Navier-Stokes equations with additive noise converge uniformly in time to Euler solutions in a 2D domain, under certain energy dissipation conditions in a boundary layer.

Contribution

It establishes the inviscid limit for stochastic Navier-Stokes equations with general initial conditions under a Kato-type boundary layer energy dissipation assumption.

Findings

Convergence in $L^2$ norm uniformly in time

Inviscid limit holds under energy dissipation assumption

Results extend to stochastic Navier-Stokes with additive noise

Abstract

We consider in a smooth and bounded two dimensional domain the convergence in the $L^2$ norm, uniformly in time, of the solution of the stochastic Navier-Stokes equations with additive noise and no-slip boundary conditions to the solution of the corresponding Euler equations. We prove, under general regularity on the initial conditions of the Euler equations, that assuming the dissipation of the energy of the solution of the Navier-Stokes equations in a Kato type boundary layer, then the inviscid limit holds.