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:

arXiv eprints
 Pub Date:
 November 2012
 arXiv:
 arXiv:1212.0036
 Bibcode:
 2012arXiv1212.0036B
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematics  Classical Analysis and ODEs;
 Primary: 35Q31;
 Secondary: 35J57
 EPrint:
 Final version incorporating referee's suggestions