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Behavior of several two-dimensional fluid equations in singular scenarios. (English) Zbl 0965.35133

Summary: 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.

MSC:

35Q35 PDEs in connection with fluid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)
35Q05 Euler-Poisson-Darboux equations
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