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

Nader Masmoudi, Frederic Rousset

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)301-417
Number of pages117
JournalArchive for Rational Mechanics and Analysis
Volume223
Issue number1
DOIs
StatePublished - Jan 1 2017

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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