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A Criterion for the Equivalence of the Birkhoff-Rott and Euler Descriptions of Vortex Sheet Evolution | M. C. Lopes Filho
; H. J. Nussenzveig Lopes
; S. Schochet
; | Date: |
10 Feb 2005 | Subject: | Analysis of PDEs MSC-class: 76B03 (Primary) 35Q35, 76B47 (Secondary) | math.AP | 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. | Source: | arXiv, math.AP/0502215 | Services: | Forum | Review | PDF | Favorites |
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