A naive parametrization for the vortex-sheet problem
Analysis of PDEs
2010-05-25 v2
Abstract
We consider the dynamics of a vortex sheet that evolves by the Birkhoff-Rott equations. The fluid evolution is understood as a weak solution of the incompressible Euler equations where the vorticity is given by a delta function on a curve multiplied by an amplitude. The solutions we study are with finite energy, which implies zero mean amplitude. In this context we choose a parametrization for the motion of the vortex sheet for which the equation is well-posed for analytic initial data. For the equation of the amplitude we show ill-posedness for non-analytic initial data.
Cite
@article{arxiv.0810.0731,
title = {A naive parametrization for the vortex-sheet problem},
author = {Angel Castro and Diego Cordoba and Francisco Gancedo},
journal= {arXiv preprint arXiv:0810.0731},
year = {2010}
}
Comments
23 pages, added a local-existence proof for analytic initial data