Homogenization of Stokes Systems with Periodic Coefficients

Author

Shu Gu, University of KentuckyFollow

Date Available

7-20-2016

Year of Publication

2016

Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation

College

Arts and Sciences

Department/School/Program

Mathematics

First Advisor

Dr. Zhongwei Shen

Abstract

In this dissertation we study the quantitative theory in homogenization of Stokes systems. We study 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 Liouville property for solutions in ℝ^d. We are able to obtain the boundary W^{1,p} estimates in a bounded C¹ domain for any 1 < p < ∞. We also study the convergence rates in L² and H¹ of Dirichlet and Neumann problems for Stokes systems with rapidly oscillating periodic coefficients, without any regularity assumptions on the coefficients.

Digital Object Identifier (DOI)

http://dx.doi.org/10.13023/ETD.2016.302

Recommended Citation

Gu, Shu, "Homogenization of Stokes Systems with Periodic Coefficients" (2016). Theses and Dissertations--Mathematics. 39.
https://uknowledge.uky.edu/math_etds/39