论文标题
由达西定律统治的不稳定流量的校正估计和同质化错误
Corrector estimates and homogenization errors of unsteady flow ruled by Darcy's law
论文作者
论文摘要
本文着重于达西定律，结合了记忆效应，研究了针对穿孔领域的非平稳stoke store方程。我们在能量标准方面为速度和压力建立了急剧的均质化误差。主要挑战在于衡量由不可压缩条件引起的边界层。为了解决这个问题，我们使用Bogovskii的操作员构建边界层校正器。同样，目前的工作还提供了这些校正器的详细规律性估计，在这些校正器中，初始值和边界值之间的不兼容引起了很大的困难。本文开发的方法具有很大的潜力，可以在均质化设置以外的其他进化模型中解决相同问题。
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.
