Global regularity for a Birkhoff-Rott-alpha approximation of the dynamics of vortex sheets of the 2D Euler equations
Analysis of PDEs
2008-07-04 v2
Abstract
We present an alpha-regularization of the Birkhoff-Rott equation, induced by the two-dimensional Euler-alpha equations, for the vortex sheet dynamics. We show that initially smooth self-avoiding vortex sheet remains smooth for all times under the alpha-regularized dynamics, provided the initial density of vorticity is an integrable function over the curve with respect to the arc-length measure.
Keywords
Cite
@article{arxiv.0709.4626,
title = {Global regularity for a Birkhoff-Rott-alpha approximation of the dynamics of vortex sheets of the 2D Euler equations},
author = {Claude Bardos and Jasmine S. Linshiz and Edriss S. Titi},
journal= {arXiv preprint arXiv:0709.4626},
year = {2008}
}
Comments
7 pages, no figures, submitted to the proceedings of the Conference EE250, corrected typos, references added