A Criterion for the Equivalence of the Birkhoff-Rott and Euler Descriptions of Vortex Sheet Evolution
Analysis of PDEs
2007-06-14 v1
Abstract
In this article we consider the evolution of vortex sheets in the plane both as a weak solution of the two dimensional incompressible Euler equations and as a (weak) solution of the Birkhoff-Rott equations. We begin by discussing the classical Birkhoff-Rott equations with respect to arbitrary parametrizations of the sheet. We introduce a notion of weak solution to the Birkhoff-Rott system and we prove consistency of this notion with the classical formulation of the equations. Our main purpose in this paper is to present a sharp criterion for the equivalence of the weak Euler and weak Birkhoff-Rott descriptions of vortex sheet dynamics.
Keywords
Cite
@article{arxiv.math/0502215,
title = {A Criterion for the Equivalence of the Birkhoff-Rott and Euler Descriptions of Vortex Sheet Evolution},
author = {M. C. Lopes Filho and H. J. Nussenzveig Lopes and S. Schochet},
journal= {arXiv preprint arXiv:math/0502215},
year = {2007}
}
Comments
22 pages