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Résumé: We present an α-regularization of the Birkhoff-Rott equation, induced by the two-dimensional Euler-α equations, for the vortex sheet dynamics. We show that initially smooth self-avoiding vortex sheet remains smooth for all times under the α-regularized dynamics, provided the initial density of vorticity is an integrable function over the curve with respect to the arc-length measure.
Mots Clés: inviscid regularization of Euler equations; Birkhoff-Rott regularization; 2D vortex sheet