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

General Mathematics
Applied Mathematics

Access to Document

10.1016/S0021-7824(99)00032-X

Cite this

@article{f8cb8a6086b94924be7bfb3ac5de8632,

title = "Incompressible limit for solutions of the isentropic Navier-Stokes equations with Dirichlet boundary conditions",

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.",

author = "B. Desjardins and E. Grenier and Lions, {P. L.} and N. Masmoudi",

year = "1999",

month = jun,

day = "10",

doi = "10.1016/S0021-7824(99)00032-X",

language = "English (US)",

volume = "78",

pages = "461--471",

journal = "Journal des Mathematiques Pures et Appliquees",

issn = "0021-7824",

publisher = "Elsevier Masson s.r.l.",

number = "5",

}

TY - JOUR

T1 - Incompressible limit for solutions of the isentropic Navier-Stokes equations with Dirichlet boundary conditions

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 - http://www.scopus.com/inward/record.url?scp=0033542301&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033542301&partnerID=8YFLogxK

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

SP - 461

EP - 471

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

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this