Abstract
We consider the Stokes equations on a bounded perforated domain completed with non-zero constant boundary conditions on the holes. We investigate configurations for which the holes are identical spheres and their number N goes to infinity while their radius aN tends to zero. Under the assumption that aN scales like a/N and that there is no concentration in the distribution of holes, we prove that the solution is well approximated asymptotically by solving a Stokes–Brinkman problem.
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Communicated by L. Saint-Raymond
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Hillairet, M. On the Homogenization of the Stokes Problem in a Perforated Domain. Arch Rational Mech Anal 230, 1179–1228 (2018). https://doi.org/10.1007/s00205-018-1268-7
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DOI: https://doi.org/10.1007/s00205-018-1268-7