Incompressible limit for solutions of the isentropic Navier-Stokes equations with Dirichlet boundary conditions

B. Desjardins; E. Grenier; P. L. Lions; N. Masmoudi

doi:10.1016/S0021-7824(99)00032-X

Incompressible limit for solutions of the isentropic Navier-Stokes equations with Dirichlet boundary conditions

B. Desjardins^*
, E. Grenier
, P. L. Lions
, N. Masmoudi

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

200 Citations (Scopus)

Abstract

We study here the limit of global weak solutions of the compressible Navier-Stokes equations (in the isentropic regime) in a bounded domain, with Dirichlet boundary conditions on the velocity, as the Mach number goes to 0. We show that the velocity converges weakly in L² to a global weak solution of the incompressible Navier-Stokes equations. Moreover, the convergence in L² is strong under some geometrical assumption on Ω.

Original language	English
Pages (from-to)	461-471
Number of pages	11
Journal	Journal des Mathematiques Pures et Appliquees
Volume	78
Issue number	5
DOIs	https://doi.org/10.1016/S0021-7824(99)00032-X
Publication status	Published - 10 Jun 1999
Externally published	Yes

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abstract = "We study here the limit of global weak solutions of the compressible Navier-Stokes equations (in the isentropic regime) in a bounded domain, with Dirichlet boundary conditions on the velocity, as the Mach number goes to 0. We show that the velocity converges weakly in L2 to a global weak solution of the incompressible Navier-Stokes equations. Moreover, the convergence in L2 is strong under some geometrical assumption on Ω.",

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AU - Desjardins, B.

AU - Grenier, E.

AU - Lions, P. L.

AU - Masmoudi, N.

PY - 1999/6/10

Y1 - 1999/6/10

N2 - We study here the limit of global weak solutions of the compressible Navier-Stokes equations (in the isentropic regime) in a bounded domain, with Dirichlet boundary conditions on the velocity, as the Mach number goes to 0. We show that the velocity converges weakly in L2 to a global weak solution of the incompressible Navier-Stokes equations. Moreover, the convergence in L2 is strong under some geometrical assumption on Ω.

AB - We study here the limit of global weak solutions of the compressible Navier-Stokes equations (in the isentropic regime) in a bounded domain, with Dirichlet boundary conditions on the velocity, as the Mach number goes to 0. We show that the velocity converges weakly in L2 to a global weak solution of the incompressible Navier-Stokes equations. Moreover, the convergence in L2 is strong under some geometrical assumption on Ω.

UR - https://www.scopus.com/pages/publications/0033542301

U2 - 10.1016/S0021-7824(99)00032-X

DO - 10.1016/S0021-7824(99)00032-X

M3 - Article

AN - SCOPUS:0033542301

SN - 0021-7824

VL - 78

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JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

IS - 5

ER -

Incompressible limit for solutions of the isentropic Navier-Stokes equations with Dirichlet boundary conditions

Abstract

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