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

We study the asymptotic behavior of solutions of the two-dimensional stochastic Navier-Stokes (SNS) equation with no-slip boundary condition in the small viscosity limit. Several equivalent dissipation conditions of the Kato type are derived to ensure that the convergence from the SNS equation to the corresponding stochastic Euler equation holds in the energy space. We do not assume any smallness on the noise of the SNS equation.