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arXiv · 1202.0657

Uniform regularity and vanishing viscosity limit for the free surface Navier-Stokes equations

Nader Masmoudi·Frédéric Rousset
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Abstract

We study the inviscid limit of the free boundary Navier-Stokes equations. We prove the existence of solutions on a uniform time interval by using a suitable functional framework based on Sobolev conormal spaces. This allows us to use a strong compactness argument to justify the inviscid limit. Our approach does not rely on the justification of asymptotic expansions. In particular, we get a new existence result for the Euler equations with free surface from the one for Navier-Stokes.

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Nader Masmoudi, Frédéric Rousset. 2012-02-03. Uniform regularity and vanishing viscosity limit for the free surface Navier-Stokes equations. https://arxiv.org/abs/1202.0657

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