A study of the three-dimensional quasi-geostrophic system
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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.