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

Nader Masmoudi; Frederic Rousset

doi:10.1007/s00205-016-1036-5

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

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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.

Original language	English (US)
Pages (from-to)	301-417
Number of pages	117
Journal	Archive for Rational Mechanics and Analysis
Volume	223
Issue number	1
DOIs	https://doi.org/10.1007/s00205-016-1036-5
State	Published - Jan 1 2017

ASJC Scopus subject areas

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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

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