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Uniform regularity for the Navier-Stokes equation with Navier boundary condition. (English) Zbl 1286.76026

Summary: We prove that there exists an interval of time which is uniform in the vanishing viscosity limit and for which the Navier-Stokes equation with the Navier boundary condition has a strong solution. This solution is uniformly bounded in a conormal Sobolev space and has only one normal derivative bounded in \(L ^{\infty }\). This allows us to obtain the vanishing viscosity limit to the incompressible Euler system from a strong compactness argument.

MSC:

76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
35Q30 Navier-Stokes equations
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