Homogenization of Stokes Systems and Uniform Regularity Estimates

Authors

Shu Gu, University of KentuckyFollow
Zhongwei Shen, University of KentuckyFollow

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^∞ estimates for the pressure as well as a Liouville property for solutions in ℝ^d. We also obtain the boundary W^1,p estimates in a bounded C¹ domain for any 1 < p < ∞.

Document Type

Article

Publication Date

2015

Notes/Citation Information

Published in SIAM Journal of Mathematical Analysis, v. 47, no. 5, p. 4025-4057.

First Published in SIAM Journal of Mathematical Analysis in v. 47, no. 5, published by the Society for Industrial and Applied Mathematics (SIAM). Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.

Digital Object Identifier (DOI)

https://doi.org/10.1137/151004033

Repository Citation

Gu, Shu and Shen, Zhongwei, "Homogenization of Stokes Systems and Uniform Regularity Estimates" (2015). Mathematics Faculty Publications. 17.
https://uknowledge.uky.edu/math_facpub/17