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Inviscid limits for the Navier-Stokes equations with Navier friction boundary conditions. (English) Zbl 1169.35365

Summary: We consider the Navier-Stokes equations with Navier friction boundary conditions and prove two results. First, in the case of a bounded domain we prove that weak Leray solutions converge (locally in time in dimension \(\geq 3\) and globally in time in dimension 2) as the viscosity goes to 0 to a strong solution of the Euler equations, provided that the initial data converge in \(L^2\) to a sufficiently smooth limit. Second, we consider the case of a half-space and anisotropic viscosities: we fix the horizontal viscosity, send the vertical viscosity to 0 and prove convergence to the expected limit system under a weaker hypothesis on the initial data.

MSC:

35Q30 Navier-Stokes equations
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
76D09 Viscous-inviscid interaction
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