Uniform Regularity and Vanishing Viscosity Limit for the Free Surface Navier–Stokes Equations

By Nader Masmoudi, Frédéric Rousset. Archive for Rational Mechanics and Analysis, 2012

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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.

Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics

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