On some electroconvection models
Peter Constantin, Tarek Elgindi, Mihaela Ignatova, Vlad Vicol
TL;DR
This paper analyzes a mathematical model of electroconvection in a two-dimensional annular smectic film, proving the existence and uniqueness of smooth solutions over time.
Contribution
It establishes the global well-posedness of a specific electroconvection model, which was previously unproven.
Findings
Proved global existence of smooth solutions
Established uniqueness of solutions over time
Model is mathematically well-posed
Abstract
We consider a model of electroconvection motivated by studies of the motion of a two dimensional annular suspended smectic film under the influence of an electric potential maintained at the boundary by two cylindrical electrodes. We prove that this electroconvection model has global in time unique smooth solutions.
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