Uniform Regularity for the Navier-Stokes Equation with Navier Boundary Condition

Nader Masmoudi, Frédéric Rousset

Research output: Contribution to journalArticle

Abstract

We prove that there exists an interval of time which is uniform in the vanishing viscosity limit and for which the Navier-Stokes equation with the Navier boundary condition has a strong solution. This solution is uniformly bounded in a conormal Sobolev space and has only one normal derivative bounded in L . This allows us to obtain the vanishing viscosity limit to the incompressible Euler system from a strong compactness argument.

Original languageEnglish (US)
Pages (from-to)529-575
Number of pages47
JournalArchive for Rational Mechanics and Analysis
Volume203
Issue number2
DOIs
StatePublished - Feb 2012

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Vanishing Viscosity
Navier Stokes equations
Navier-Stokes Equations
Regularity
Boundary conditions
Viscosity
Euler System
Sobolev spaces
Strong Solution
Sobolev Spaces
Compactness
Derivatives
Derivative
Interval

ASJC Scopus subject areas

  • Analysis
  • Mechanical Engineering
  • Mathematics (miscellaneous)

Cite this

Uniform Regularity for the Navier-Stokes Equation with Navier Boundary Condition. / Masmoudi, Nader; Rousset, Frédéric.

In: Archive for Rational Mechanics and Analysis, Vol. 203, No. 2, 02.2012, p. 529-575.

Research output: Contribution to journalArticle

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