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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.
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