On the homogenization of the Stokes problem in a perforated domain

Matthieu Hillairet (1)

1 IMAG - Institut Montpelliérain Alexander Grothendieck

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 there is no concentration in the distribution of holes, 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. Archive for Rational Mechanics and Analysis, 2018, 230 (3), pp.1179-1228. ⟨10.1007/s00205-018-1268-7⟩. ⟨hal-01302560v4⟩