Homogenization of a Stokes flow in Porous Media under a Non-homogeneous Slip Boundary Condition

Résumé

We deal with the Stokes problem in a domain of R N, N > 2, that is ε-periodically perforated by holes of sizes r1(εδ1) = o(ε) and r2(εδ2) = o(ε). A Robin-type condition depending on a parameter γ is prescribed on the boundary of some holes while a Dirichlet condition is imposed on the boundary of the remainding holes as well as on the external boundary of the domain. Our aim is to describe the asymptotic behavior of the fluid’s velocity and pressure as ε tends to zero and derive the limit problem. To achieve this, we use the unfolding method introduced by Cioranescu et al. (C. R. Acad. Sci. Paris, Ser. I 335 (2002) 99-104