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Valeria 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
Article PDF
Class. Math.: 76B47, 35Q35, 35Q55, 35B35, 35P25
Mots clés: Vortex filaments, selfsimilar solutions, Schrödinger equations, scattering

Résumé - Abstract

Dans cet article de comptes rendus on présente une série de résultats sur la stabilité des solutions auto-similaires de l’équation du tourbillon filamentaire. Cette équation décrit un flot de courbes de $\mathbb{R}^3$ et est utilisée comme modèle pour l’évolution d’un tourbillon filamentaire dans un fluide. Le théorème principal donne, sous des hypothèses appropriées, l’existence et la description des solution engendrées par des courbes à un coin, sur temps positifs et négatifs. Le théorème compagnon décrit l’évolution des perturbations des solutions auto-similaires jusque’à formation d’une singularité en temps fini, et au-delà de ce temps. On va donner une esquisse des preuves. Ces résultats on été obtenus en collaboration avec Luis Vega.

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