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. We start from a brief introduction to homogenization theory, and then move to the ideas of non-standard two-scale expansions. To obtain the optimal error, we 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. As a result, we further explain how we handle the boundary-layer correctors associated with Bogovskii’s operator.
This work is joint with Dr Li Wang and Prof. Zhifei Zhang in Peking University.
This video was produced by the SITE Research Center at New York University, as part of their talk series.
