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Dissertation
Regularity estimates for the Navier-Stokes equations and a class of degenerate equations
University of Iowa
Doctor of Philosophy (PhD), University of Iowa
Spring 2023
DOI: 10.25820/etd.007164
Abstract
In this project, we study the regularity of two different types of partial differential equations.
We investigate Holder regularity for the nonlinear Navier-Stokes equations up to a C3 boundary. We find suitable weak solutions are regular up to a set of Hausdorff dimension 1. We use a modified compactness method and monotonicity properties of harmonic functions.
We also investigate W1,p estimates for a class of degenerate partial differential equations of subelliptic type a where a is a positive real number. We use the method of compactness established by De Giorgi when studying the Plateau problem of minimal surfaces.
Details
- Title: Subtitle
- Regularity estimates for the Navier-Stokes equations and a class of degenerate equations
- Creators
- Bryanna Petentler
- Contributors
- Lihe Wang (Advisor)Rodica Curtu (Committee Member)Palle Jorgensen (Committee Member)Tong Li (Committee Member)Gerhard Strohmer (Committee Member)Xiaoyi Zhang (Committee Member)
- Resource Type
- Dissertation
- Degree Awarded
- Doctor of Philosophy (PhD), University of Iowa
- Degree in
- Mathematics
- Date degree season
- Spring 2023
- Publisher
- University of Iowa
- DOI
- 10.25820/etd.007164
- Number of pages
- vii, 67 pages
- Copyright
- Copyright 2023 Bryanna Petentler
- Language
- English
- Date submitted
- 04/21/2023
- Date approved
- 05/09/2023
- Description bibliographic
- Includes bibliographical references.
- Academic Unit
- Mathematics
- Record Identifier
- 9984425391202771
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