The Euler Equations in planar nonsmooth convex domains
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.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2012
- DOI:
- 10.48550/arXiv.1212.0036
- arXiv:
- arXiv:1212.0036
- Bibcode:
- 2012arXiv1212.0036B
- Keywords:
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- Mathematics - Analysis of PDEs;
- Mathematics - Classical Analysis and ODEs;
- Primary: 35Q31;
- Secondary: 35J57
- E-Print:
- Final version incorporating referee's suggestions