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

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

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 (US)
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
State	Published - Jun 10 1999

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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AU - Grenier, E.

AU - Lions, P. L.

AU - Masmoudi, N.

PY - 1999/6/10

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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.

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

Abstract

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