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Table of contents for this volume | Next articleValeria Banica
Evolution by the vortex filament equation of curves with a corner
(Évolution par l’équation du tourbillon filamentaire de courbes à un coin)
Journées équations aux dérivées partielles (2013), Exp. No. 1, 18 p., doi: 10.5802/jedp.97
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Class. Math.: 76B47, 35Q35, 35Q55, 35B35, 35P25
Keywords: Vortex filaments, selfsimilar solutions, Schrödinger equations, scattering
Résumé - Abstract
In this proceedings article we shall survey a series of results on the stability of self-similar solutions of the vortex filament equation. This equation is a geometric flow for curves in $\mathbb{R}^3$ and it is used as a model for the evolution of a vortex filament in fluid mechanics. The main theorem give, under suitable assumptions, the existence and description of solutions generated by curves with a corner, for positive and negative times. Its companion theorem describes the evolution of perturbations of self-similar solutions up to a singularity formation in finite time, and beyond this time. We shall give a sketch of the proof. These results were obtained in collaboration with Luis Vega.
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