Mathematics of Fluid Motion: A Priori Bounds with a Twist

Chris Hallstrom

For more than 170 years, the differential equations that describe fluid motion have been one of the most active and challenging topics in applied mathematics. Indeed, even fundamental questions such as the existence and uniqueness of solutions have yet to be fully resolved. In this talk, I will describe a simple model for convection in a rotating fluid and outline some of the mathematical difficulties that arise in the analysis of such a system. Of particular interest will be the problem of deriving {\it a priori} bounds from the equations in a way that captures the influence of key parameters in the equations.