Smooth compactly supported vortex layers around any closed analytic curve evolve, in the zero-thickness limit, according to the Birkhoff-Rott equations.
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Desingularization of vortex sheets for the 2D Euler equations
Smooth compactly supported vortex layers around any closed analytic curve evolve, in the zero-thickness limit, according to the Birkhoff-Rott equations.