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

^*此作品的通讯作者

École normale supérieure
École normale supérieure de Lyon
Université Paris Dauphine

科研成果: 期刊稿件 › 文章 › 同行评审

205 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	461-471
页数	11
期刊	Journal des Mathematiques Pures et Appliquees
卷	78
期	5
DOI	https://doi.org/10.1016/S0021-7824(99)00032-X
出版状态	已出版 - 10 6月 1999
已对外发布	是

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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

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

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