The Euler Equations in planar nonsmooth convex domains
Analysis of PDEs
2013-08-19 v2 Classical Analysis and ODEs
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.
Cite
@article{arxiv.1212.0036,
title = {The Euler Equations in planar nonsmooth convex domains},
author = {Claude Bardos and Francesco Di Plinio and Roger Temam},
journal= {arXiv preprint arXiv:1212.0036},
year = {2013}
}
Comments
Final version incorporating referee's suggestions