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

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

Received: 5 February 2002
Revised: 5 March 2002

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”.