Homogenization of Stokes equations in perforated domains: a unified approach

Abstract

We consider the homogenization of the Stokes equations in a domain perforated with a large number of small holes which are periodically distributed. In [1,2], Allaire 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 [17].