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

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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".

Original languageEnglish (US)
Pages (from-to)885-906
Number of pages22
JournalESAIM - Control, Optimisation and Calculus of Variations
Volume8
DOIs
StatePublished - Jun 2002

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Porous Medium Equation
Compressible Navier-Stokes Equations
Navier-Stokes System
Homogenization
Dirichlet Boundary Conditions
Navier Stokes equations
Porous Media
Porous materials
Scaling
Boundary conditions

Keywords

  • Compressible Navier-Stokes
  • Homogenization
  • Porous medium equation

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

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title = "Homogenization of the compressible Navier-stokes equations in a porous medium",
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-Stokes, Homogenization, Porous medium equation",
author = "Nader Masmoudi",
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journal = "ESAIM - Control, Optimisation and Calculus of Variations",
issn = "1292-8119",
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AB - 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".

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KW - Homogenization

KW - Porous medium equation

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JO - ESAIM - Control, Optimisation and Calculus of Variations

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