Abstract: We consider the Stokes problem in a domain Ωεδ1δ2 of RN, N⩾3 ε-periodically perforated by holes of size r1(εδ1) and r2(εδ2) (ε, δ1=δ1(ε), δ2=δ2(ε) being small parameters), with r1(εδ1)/ε→0 and r2(εδ2)/ε→0 as ε→0. Our aim is to describe the asymptotic behavior of the velocity and the pressure of the fluid as ε→0 and give, if possible, a limit (“homogenized”) problem. To do so, we use the periodic unfolding method introduced by Cioranescu, Damlamian and Griso (C. R. Acad. Sci. Paris, Ser. I 335 (2002) 99–104; SIAM J. of Math. Anal. 40(4) (2008) 1585–1620). It allow us to consider a general geometric framework and so, to extend the results from Cioranescu, Donato and Ene (Math. Models and Methods in Appl. Sciences 19 (1996) 857–881) and Capatina and Ene (European J. of Math. 22 (2011) 333–345).
Keywords: Stokes problem, Robin condition, unfolding method
