Corrector estimates and homogenization errors of unsteady flow ruled by Darcy's law
Abstract
Focusing on Darcy's law incorporating memory effects, this paper studies non-stationary Stokes equations on perforated domains. We establish a sharp homogenization error for both velocity and pressure in terms of the energy norm. The main challenge lies in gauging the boundary layers induced by the incompressibility condition. To address this, we construct boundary-layer correctors using Bogovskii's operator. Also, the present work provides detailed regularity estimates for these correctors, where a significant difficulty arises from the incompatibility between initial and boundary values. The methodologies developed herein hold great potential for tackling the same issue in other evolutionary models beyond a homogenization setting.
Keywords
Cite
@article{arxiv.2202.04826,
title = {Corrector estimates and homogenization errors of unsteady flow ruled by Darcy's law},
author = {Li Wang and Qiang Xu and Zhifei Zhang},
journal= {arXiv preprint arXiv:2202.04826},
year = {2025}
}
Comments
42 pages. Compared to the previous version arXiv:2202.04826v1 (2022), we now turn to make more in-depth use of the antisymmetry property of the flux corrector. This improvement greatly simplifies the decomposition process for boundary layers. Welcome comments from readers