Uniform Regularity for the Navier-stokes Equation with Navier Boundary Condition

@inproceedings{MasmoudiUniformRF,
  title={Uniform Regularity for the Navier-stokes Equation with Navier Boundary Condition},
  author={Nader Masmoudi and Frederic Rousset}
}
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 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 ∞. This allows to get the vanishing viscosity limit to the incompressible Euler system from a strong compactness argument. 

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