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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|
|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.|
|Editor:||Amer Mathematical Soc|
|Appears in Collections:||Artigos e Materiais de Revistas Científicas - Unicamp|
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