English

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