The Inviscid Limit for the Navier–Stokes Equations with Slip Condition on Permeable Walls

Abstract

We consider the Navier–Stokes equations in a 2D-bounded domain with general non-homogeneous Navier slip boundary conditions prescribed on permeable boundaries, and study the vanishing viscosity limit. We prove that solutions of the Navier–Stokes equations converge to solutions of the Euler equations satisfying the same Navier slip boundary condition on the inflow region of the boundary. The convergence is strong in Sobolev’s spaces \(W^{1}_{p}, p>2\), which correspond to the spaces of the data.