Behavior of several two-dimensional fluid equations in singular scenarios.
We give conditions that rule out formation of sharp fronts for certain two-dimensional incompressible flows. We show that a necessary condition of having a sharp front is that the flow has to have uncontrolled velocity growth. In the case of the quasi-geostrophic equation and two-dimensional Euler equation, we obtain estimates on the formation of semi-uniform fronts.
University of Chicago, Chicago, IL 60637, USA.
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Cordoba
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Fefferman