2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164092We present an alpha-regularization of the Birkhoff-Rott equation, induced by the two-dimensional Euler-alpha equations, for the vortex sheet dynamics. We show that initially smooth self-avoiding vortex sheet remains smooth for all times under the alpha-regularized dynamics, provided the initial density of vorticity is an integrable function over the curve with respect to the arc-length measure.7 pages, no figures, submitted to the proceedings of the Conference EE250, corrected typos, references addedAnalysis of PDEs76B03 (Primary); 35Q35, 76B47 (Secondary)text