A Criterion for the Equivalence of the Birkhoff-Rott and Euler Descriptions of Vortex Sheet Evolution

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dc.creatorFilho, M. C. Lopes
dc.creatorLopes, H. J. Nussenzveig
dc.creatorSchochet, S.
dc.date2005-02-10
dc.date.accessioned2026-07-07T08:09:56Z
dc.date.available2026-07-07T08:09:56Z
dc.descriptionIn 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.
dc.description22 pages
dc.identifierhttps://arxiv.org/abs/math/0502215
dc.identifierhttp://arxiv.org/abs/math/0502215
dc.identifierTransactions of the A. M. S., v. 359 (2007), 4125--4142
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/131691
dc.subjectAnalysis of PDEs
dc.subject76B03 (Primary) 35Q35, 76B47 (Secondary)
dc.titleA Criterion for the Equivalence of the Birkhoff-Rott and Euler Descriptions of Vortex Sheet Evolution
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