Author ORCID Identifier
Date Available
5-11-2024
Year of Publication
2024
Degree Name
Doctor of Philosophy (PhD)
Document Type
Doctoral Dissertation
College
Arts and Sciences
Department/School/Program
Mathematics
First Advisor
Dr. Zhongwei Shen
Abstract
We consider the Stokes equations in an unbounded domain $\omega_{\epsilon,\eta}$ perforated by small obstacles, where $\epsilon$ represents the minimal distance between obstacles and $\eta$ is the ratio between the obstacle size and $\epsilon$. We are able to obtain uniform $W^{1,q}$ estimates for solutions to the Stokes equations in such domains with bounding constants depending explicitly on $\epsilon$ and $\eta$.
Digital Object Identifier (DOI)
https://doi.org/10.13023/etd.2024.158
Funding Information
This research was funded by National Science Foundation Division of Mathematical Sciences (no. 1856235) in 2020 and 2021 and National Science Foundation Division of Mathematical Sciences (no. 2153585) in 2022 and 2023.
Recommended Citation
Wallace, Jamison R., "Uniform Regularity Estimates for the Stokes System in Perforated Domains" (2024). Theses and Dissertations--Mathematics. 113.
https://uknowledge.uky.edu/math_etds/113
