Long time dynamics of a model of electroconvection

Abdo, Elie; Ignatova, Mihaela

doi:10.1090/tran/8394

Long time dynamics of a model of electroconvection
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by Elie Abdo and Mihaela Ignatova PDF

Trans. Amer. Math. Soc. 374 (2021), 5849-5875 Request permission

Abstract:

We study a model of electroconvection in which a two dimensional viscous fluid caries electrical charges and interacts with them. The system has global solutions, but in general the solutions do not have bounded mean. Tracking the mean, we associate to each solution a mean zero frame and show that in the mean zero frame the system has a compact, finite dimensional global attractor. If the fluid is forced only by electrical forces and no other body forces are present, then the attractor reduces to one point.

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