Homogenization of Stokes Systems and Uniform Regularity Estimates

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

Keywords

• STOKES SYSTEMS
• UNIFORM REGULARITY
• REGULARITY ESTIMATES
• PERIODIC COEFFICIENTS
• LIOUVILLE PROPERTY
• RAPIDLY OSCILLATING
• INTERIOR LIPSCHITZ
• LIPSCHITZ ESTIMATES

Other Versions

• Version 2, 2015-01-14, preprints

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