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Title:
Long Time Behavior of Electroconvection Models
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Abstract:
We present two electroconvection models describing the interaction between a surface charge density and a fluid in a two-dimensional situation. We compare these models with the surface quasi-geostrophic equation in bounded domains and recall some recent results. For the first model, the global existence results can be obtained for bounded domains and for the torus. In the latter case, in joint work with graduate student E. Abdo, we proved that the long time asymptotic state of the system is finite dimensional, if body forces are applied to the fluid, and a singleton solution in the absence of fluid body forces. In the whole space, in the absence of forcing, we obtain optimal decay rates. For the more challenging second model, corresponding to electroconvection through porous media, we proved global existence for subcritical and for small data cases.
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