Corrector estimates and homogenization error of unsteady flow ruled by Darcy's law

Abstract

Concerned with Darcy's law with memory, originally developed by J.-L. Lions [28], this paper is devoted to studying non-stationary Stokes equations on perforated domains. We obtain a sharp homogenization error in the sense of energy norms, where the main challenge is to control the boundary layers caused by the incompressibility condition. Our method is to construct boundarylayer correctors associated with Bogovskii's operator, which is robust enough to be applied to other problems of fluid mechanics on homogenization and porous medium.