On the homogenization of the Stokes problem in a perforated domain

Matthieu Hillairet

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arXiv · 1604.04379

On the homogenization of the Stokes problem in a perforated domain

Matthieu Hillairet

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Abstract

We consider the Stokes equations on a bounded perforated domaincompleted with non-zero constant boundary conditions on the holes. We investigate configurations forwhich the holes are identical spheres and their number N goes to infinity while their radius1/N tends to zero. We prove that, under the assumption that there is no concentrationin the distribution of holes, the solution is well approximated asymptotically by solving aStokes-Brinkman problem.

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Matthieu Hillairet. 2016-04-15. On the homogenization of the Stokes problem in a perforated domain. https://arxiv.org/abs/1604.04379

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