Remarks on the inviscid limit for the Navier-Stokes equations for uniformly bounded velocity fields

Peter Constantin; Tarek Elgindi; Mihaela Ignatova; Vlad Vicol

doi:10.1137/15M1054572

Remarks on the inviscid limit for the Navier-Stokes equations for uniformly bounded velocity fields

Peter Constantin, Tarek Elgindi, Mihaela Ignatova, Vlad Vicol

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23 Scopus citations

Abstract

We consider the vanishing viscosity limit of the Navier-Stokes equations in a half-plane, with Dirichlet boundary conditions. We prove that the inviscid limit holds in the energy norm if the product of the components of the Navier-Stokes solutions are equicontinuous at x₂ = 0. A sufficient condition for this to hold is that the tangential Navier-Stokes velocity remains uniformly bounded and has a uniformly integrable tangential gradient near the boundary.

Original language	English (US)
Pages (from-to)	1932-1946
Number of pages	15
Journal	SIAM Journal on Mathematical Analysis
Volume	49
Issue number	3
DOIs	https://doi.org/10.1137/15M1054572
State	Published - 2017

All Science Journal Classification (ASJC) codes

Analysis
Computational Mathematics
Applied Mathematics

Keywords

Euler equations
Inviscid limit
Navier-Stokes equations

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10.1137/15M1054572

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abstract = "We consider the vanishing viscosity limit of the Navier-Stokes equations in a half-plane, with Dirichlet boundary conditions. We prove that the inviscid limit holds in the energy norm if the product of the components of the Navier-Stokes solutions are equicontinuous at x2 = 0. A sufficient condition for this to hold is that the tangential Navier-Stokes velocity remains uniformly bounded and has a uniformly integrable tangential gradient near the boundary.",

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AU - Constantin, Peter

AU - Elgindi, Tarek

AU - Ignatova, Mihaela

AU - Vicol, Vlad

PY - 2017

Y1 - 2017

N2 - We consider the vanishing viscosity limit of the Navier-Stokes equations in a half-plane, with Dirichlet boundary conditions. We prove that the inviscid limit holds in the energy norm if the product of the components of the Navier-Stokes solutions are equicontinuous at x2 = 0. A sufficient condition for this to hold is that the tangential Navier-Stokes velocity remains uniformly bounded and has a uniformly integrable tangential gradient near the boundary.

AB - We consider the vanishing viscosity limit of the Navier-Stokes equations in a half-plane, with Dirichlet boundary conditions. We prove that the inviscid limit holds in the energy norm if the product of the components of the Navier-Stokes solutions are equicontinuous at x2 = 0. A sufficient condition for this to hold is that the tangential Navier-Stokes velocity remains uniformly bounded and has a uniformly integrable tangential gradient near the boundary.

KW - Euler equations

KW - Inviscid limit

KW - Navier-Stokes equations

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JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

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ER -

Remarks on the inviscid limit for the Navier-Stokes equations for uniformly bounded velocity fields

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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