Homogenization of Stokes Equations in Perforated Domains: A Unified Approach

We consider the homogenization of the Stokes equations in a domain perforated with a large number of small holes which are periodically distributed. Allaire (Arch Ration Mech Anal 113(3):209–259, 1990, Arch Ration Mech Anal 113(3):261–298 1990), gave a systematic study on this problem. In this paper, we introduce a unified proof for different sizes of holes for the homogenization of the Stokes equations by employing a generalized cell problem inspired by Tartar (in: Sánchez-Palencia (ed) Nonhomogeneous media and vibration theory, 1980).