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Concerned with Darcy's law with memory, originally developed by J.-L. Lions\cite{Lions81}, this paper is devoted to studying non-stationary Stokesequations on perforated domains. We obtain a sharp homogenization error in thesense of energy norms, where the main challenge is to control the boundarylayers caused by the incompressibility condition. Our method is to constructboundary-layer correctors associated with Bogovskii's operator, which is robustenough to be applied to other problems of fluid mechanics on homogenization andporous medium.

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