Behavior of several two-dimensional fluid equations in singular scenarios.

Cordoba, D; Fefferman, C · Proc Natl Acad Sci U S A · 2001

basic_science · Level V

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Abstract

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.