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

Nader Masmoudi; Frédéric Rousset

doi:10.1007/s00205-011-0456-5

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

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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 language	English (US)
Pages (from-to)	529-575
Number of pages	47
Journal	Archive for Rational Mechanics and Analysis
Volume	203
Issue number	2
DOIs	https://doi.org/10.1007/s00205-011-0456-5
State	Published - Feb 2012

ASJC Scopus subject areas

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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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.",

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AB - 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.

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

Abstract

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