Uniform regularity for the Navier-Stokes equation with Navier boundary condition

Details Uniform regularity for the Navier-Stokes equation with Navier boundary condition Uniform regularity for the Navier-Stokes equation with Navier boundary condition

2010-08-10

arxiv.org/abs/1008.1678v1

Mathematics

Analysis of PDEs

Scientific paper

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 $L^\infty$. This allows to get the vanishing viscosity limit to the incompressible Euler system from a strong compactness argument.

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