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$L^{p}$ ESTIMATES FOR THE HOMOGENIZATION OF STOKES PROBLEM IN A PERFORATED DOMAIN

Part of: Incompressible viscous fluids Basic methods in fluid mechanics Partial differential equations

Published online by Cambridge University Press:  10 April 2018

Amina Mecherbet  and
Matthieu Hillairet
Amina Mecherbet
Affiliation:
Institut Montpelliérain Alexander Grothendieck, Université de Montpellier, CNRS, Place Eugène Bataillon, 34090 Montpellier, France (amina.mecherbet@umontpellier.fr; matthieu.hillairet@umontpellier.fr)
Matthieu Hillairet
Affiliation:
Institut Montpelliérain Alexander Grothendieck, Université de Montpellier, CNRS, Place Eugène Bataillon, 34090 Montpellier, France (amina.mecherbet@umontpellier.fr; matthieu.hillairet@umontpellier.fr)
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Abstract

In this paper, we consider the Stokes equations in a perforated domain. When the number of holes increases while their radius tends to 0, it is proven in Desvillettes et al. [J. Stat. Phys. 131 (2008) 941–967], under suitable dilution assumptions, that the solution is well approximated asymptotically by solving a Stokes–Brinkman equation. We provide here quantitative estimates in $L^{p}$-norms of this convergence.

Keywords

Stokes equationshomogenizationsuspension flows

MSC classification

Primary: 76D07: Stokes and related (Oseen, etc.) flows 76M50: Homogenization 35B27: Homogenization; equations in media with periodic structure
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 19 , Issue 1 , January 2020 , pp. 231 - 258
Copyright
© Cambridge University Press 2018 

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