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arXiv · 1501.03392

Homogenization of Stokes Systems and Uniform Regularity Estimates

Shu Gu·Zhongwei Shen
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Abstract

This paper is concerned with uniform regularity estimates for a family of Stokes systems with rapidly oscillating periodic coefficients. We establish interior Lipschitz estimates for the velocity and $L^\infty$ estimates for the pressure as well as a Liouville property for solutions in $\mathbb{R}^d$. We also obtain the boundary $W^{1,p}$ estimates in a bounded $C^1$ domain for any $1<p<\infty$.

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Shu Gu, Zhongwei Shen. 2015-01-14. Homogenization of Stokes Systems and Uniform Regularity Estimates. https://arxiv.org/abs/1501.03392

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