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

Citation:
Chemetov, N. V., and F. Cipriano. "The Inviscid Limit for the Navier-Stokes Equations with Slip Condition on Permeable Walls." JOURNAL OF NONLINEAR SCIENCE. 23 (2013): 731-750.

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 , which correspond to the spaces of the data.}

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