On Kato's conditions for the inviscid limit of the two-dimensional stochastic Navier-Stokes equation

TL;DR

This paper investigates the behavior of solutions to the 2D stochastic Navier-Stokes equation as viscosity approaches zero, focusing on boundary layer effects and dissipation conditions without assuming small noise.

Contribution

It establishes new dissipation conditions for convergence in the energy space without requiring noise smallness, advancing understanding of the inviscid limit under stochastic influences.

Findings

Derived equivalent dissipation conditions for convergence

Analyzed boundary layer effects in stochastic setting

Proved convergence without small noise assumption

Abstract

We study the asymtotic behavior of solutions to the two-dimensional stochasitc Navier-Stokes (SNS) equation in the small viscosity limit. The SNS equation is supplemented with no-slip boundary condition, in which a strong boundary layer shall appear in the limit due to the mismatch of the boundary conditions of the SNS equation and the corresponding limit problem. Several equivalent dissipation conditions are derived to ensure the convergence hold in the energy space. One novelty of this work is that we do not assume any smallness for the noise.