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Homogenization of the compressible Navier–Stokes equations in a porous medium

Published online by Cambridge University Press:  15 August 2002

Nader Masmoudi
Nader Masmoudi*
Affiliation:
Courant Institute, 251 Mercer Street, New York, NY 10012, USA; masmoudi@cims.nyu.edu. Partially supported by NSF grant and an Alfred Sloan fellowship.
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Abstract

We study the homogenization of the compressible Navier–Stokes system in a periodic porous medium (of period ε) with Dirichlet boundary conditions. At the limit, we recover different systems depending on the scaling we take. In particular, we rigorously derive the so-called “porous medium equation”.

Keywords

Compressible Navier–Stokeshomogenizationporous medium equation.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 8: A tribute to JL Lions , 2002 , pp. 885 - 906
Copyright
© EDP Sciences, SMAI, 2002

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