Analysis in Mixed Norm Spaces and Application to Nonlinear Partial Differential Equations

Author

Timothy Robertson, University of Tennessee, KnoxvilleFollow

Date of Award

12-2022

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

Tuoc Phan

Committee Members

Tuoc Phan, Suzanne Lenhart, Grozdena Todorova, Michael Frazier, Hoang Tran, Thanh Do

Abstract

The goal of this dissertation is to study partial differential equations in mixed norm and weighted mixed norm spaces. This entails the development of certain analytical tools, such as estimates of the heat semigroup in the weighted mixed norm space. Using these results we extend Masuda's uniqueness theorem for the Navier-Stokes equations to general mixed norm spaces, show the existence of mild solutions to the Keller-Segel model in weighted mixed norm spaces, and uniqueness of solutions the Keller-Segel model in a special case.

Recommended Citation

Robertson, Timothy, "Analysis in Mixed Norm Spaces and Application to Nonlinear Partial Differential Equations. " PhD diss., University of Tennessee, 2022.
https://trace.tennessee.edu/utk_graddiss/11566