Homogenization of Poisson and Stokes equations in the whole space

Abstract

We consider the homogenization of the Poisson and the Stokes equations in the whole space perforated with periodically distributed small holes. The periodic homogenization in bounded domains is well understood, following the classical results in [24, 4, 1, 2]. In this paper, we show that these classical homogenization results in a bounded domain can be extended to the whole space ${\mathbb{R}}^d$. Our results cover all three cases corresponding to different sizes of holes and cover all $d\ge 2$.

arXiv comment23 pages

References in corpus (4)

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• On the derivation of a Stokes-Brinkman problem from Stokes equations around a random array of moving spheres
• Uniform estimates for Stokes equations in a domain with a small hole and applications in homogenization problems
• Homogenization of Stokes equations in perforated domains: a unified approach