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Type: Artigo de periódico
Title: A criterion for the equivalence of the Birkhoff-Rott and Euler descriptions of vortex sheet evolution
Author: Filho, MCL
Lopes, HJN
Schochet, S
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.
Subject: vortex sheets
incompressible flow
ideal flow
weak solutions
Country: EUA
Editor: Amer Mathematical Soc
Rights: aberto
Date Issue: 2007
Appears in Collections:Unicamp - Artigos e Outros Documentos

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