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

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## Abstract

We consider the Navier-Stokes equations in a 2D-bounded domain with general \textit{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.
Original language Unknown 731-750 Journal Of Nonlinear Science 23 5 https://doi.org/10.1007/s00332-013-9166-5 Published - 1 Jan 2013