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

Masmoudi, Nader

ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 885-906.

We study the homogenization of the compressible Navier-Stokes system in a periodic porous medium (of period $\epsilon$) 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”.

Classification : 76M50
Mots clés : compressible Navier-Stokes, homogenization, porous medium equation

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