Homogenization error of unsteady flow ruled by Darcy's law

Abstract

This talk is devoted to studying homogenization error for non-stationary Stokes equations on perforated domains, which originally developed by J.-L. Lions. We now present a sharp error estimate in the sense of energy norms, where the main challenge is to control the boundary layers caused by the incompressibility condition. To obtain the optimal error, we first introduce some refined regularity estimates for corrector without compatibility conditions between initial and boundary data, as well as, the well posedness of the effective equations in Bochner space. Then, we further explain how we handle the boundary-layer correctors associated with Bogovskii's operator. This work is cooperated with Dr. Li Wang and Prof. Zhifei Zhang in Peking University.