On the homogenization of the Stokes problem in a perforated domain

Matthieu Hillairet (1)

1 UM - Université de Montpellier

In this paper 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 1/N tends to zero. We prove that, under the assumption that the holes do not concentrate in any box of size 1/N^(1/3), the solution is well approximated asymptotically by solving a Stokes-Brinkman problem.

Domaines: Equations aux dérivées partielles [math.AP]

Matthieu Hillairet. On the homogenization of the Stokes problem in a perforated domain. 2016. ⟨hal-01302560v1⟩