A Study of the Three-Dimensional Quasi-Geostrophic System
[Thesis]
Novack, Matthew Dominick
Vasseur, Alexis
The University of Texas at Austin
2019
205
Ph.D.
The University of Texas at Austin
2019
The three-dimensional quasi-geostrophic system is a set of equations used to model atmospheric and oceanic circulation. We shall consider both inviscid and viscous variations of the underlying model, which may be posed on a variety of spatial domains. As is typical of models from fluid mechanics, questions of well-posedness are physically relevant and mathematically interesting. In this work, we study physical properties of the quasi-geostrophic system using modern tools from pure and applied mathematics including regularity theory, asymptotic analysis, and convex integration.