On the inviscid limit of the navier-stokes equations

Peter Constantin; Igor Kukavica; Vlad Vicol

doi:10.1090/S0002-9939-2015-12638-X

On the inviscid limit of the navier-stokes equations

Peter Constantin, Igor Kukavica, Vlad Vicol

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53 Scopus citations

Abstract

We consider the convergence in the L2 norm uniformly in time of the Navier-Stokes equations with Dirichlet boundary conditions to the Euler equations with slip boundary conditions We prove that if the Oleinik conditions of no back-flow in the trace of the Euler flow and of a lower bound for the Navier-Stokes vorticity is assumed in a Kato-like boundary layer then the inviscid limit holds.

Original language	English (US)
Pages (from-to)	3075-3090
Number of pages	16
Journal	Proceedings of the American Mathematical Society
Volume	143
Issue number	7
DOIs	https://doi.org/10.1090/S0002-9939-2015-12638-X
State	Published - 2015

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Keywords

Boundary layer
Euler equations
Inviscid limit
Navier-Stokes equations

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10.1090/S0002-9939-2015-12638-X

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abstract = "We consider the convergence in the L2 norm uniformly in time of the Navier-Stokes equations with Dirichlet boundary conditions to the Euler equations with slip boundary conditions We prove that if the Oleinik conditions of no back-flow in the trace of the Euler flow and of a lower bound for the Navier-Stokes vorticity is assumed in a Kato-like boundary layer then the inviscid limit holds.",

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AU - Kukavica, Igor

AU - Vicol, Vlad

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N2 - We consider the convergence in the L2 norm uniformly in time of the Navier-Stokes equations with Dirichlet boundary conditions to the Euler equations with slip boundary conditions We prove that if the Oleinik conditions of no back-flow in the trace of the Euler flow and of a lower bound for the Navier-Stokes vorticity is assumed in a Kato-like boundary layer then the inviscid limit holds.

AB - We consider the convergence in the L2 norm uniformly in time of the Navier-Stokes equations with Dirichlet boundary conditions to the Euler equations with slip boundary conditions We prove that if the Oleinik conditions of no back-flow in the trace of the Euler flow and of a lower bound for the Navier-Stokes vorticity is assumed in a Kato-like boundary layer then the inviscid limit holds.

KW - Boundary layer

KW - Euler equations

KW - Inviscid limit

KW - Navier-Stokes equations

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On the inviscid limit of the navier-stokes equations

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All Science Journal Classification (ASJC) codes

Keywords

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