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arXiv · 1008.1678

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

Nader Masmoudi·Frederic Rousset
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Abstract

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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Nader Masmoudi, Frederic Rousset. 2010-08-10. Uniform regularity for the Navier-Stokes equation with Navier boundary condition. https://doi.org/10.1007/s00205-011-0456-5

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