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)1-117
Number of pages117
JournalArchive for Rational Mechanics and Analysis
DOIs
StateAccepted/In press - Sep 7 2016

Fingerprint

Inviscid Limit
Vanishing Viscosity
Sobolev spaces
Euler equations
Free Surface
Navier-Stokes Equations
Regularity
Viscosity
Navier-Stokes
Free Boundary
Euler Equations
Justification
Justify
Sobolev Spaces
Existence Results
Compactness
Asymptotic Expansion
Existence of Solutions
Interval
Framework

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Cite this

Uniform Regularity and Vanishing Viscosity Limit for the Free Surface Navier–Stokes Equations. / Masmoudi, Nader; Rousset, Frederic.

In: Archive for Rational Mechanics and Analysis, 07.09.2016, p. 1-117.

Research output: Contribution to journalArticle

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