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

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