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arXiv · 1212.0036

The Euler Equations in planar nonsmooth convex domains

Claude Bardos·Francesco Di Plinio·Roger Temam
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Abstract

We consider the Euler system set on a bounded convex planar domain, endowed with impermeability boundary conditions. This system is a model for the barotropic mode of the Primitive Equations on a rectangular domain. We show the existence of weak solutions with L^p vorticity for 4/3<= p <= 2, extending and enriching a previous result of Taylor. In the physically interesting case of a rectangular domain, a similar result holds for all 2<p<\infty as well. Moreover, we show the uniqueness of solutions with bounded initial vorticity. The main tool is a new BMO regularity estimate for the Dirichlet problem on domains with corners.

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Claude Bardos, Francesco Di Plinio, Roger Temam. 2013-08-16. The Euler Equations in planar nonsmooth convex domains. https://doi.org/10.1016/j.jmaa.2013.05.005

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