Evolution by the vortex filament equation of curves with a corner

Valeria Banica[1]

  • [1] Laboratoire Analyse et probabilités (EA 2172), Déptartement de Mathématiques, Université d’Évry, 23 Bd. de France, 91037 Évry, France

Journées Équations aux dérivées partielles (2013)

  • page 1-18
  • ISSN: 0752-0360

Abstract

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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 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.

How to cite

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Banica, Valeria. "Evolution by the vortex filament equation of curves with a corner." Journées Équations aux dérivées partielles (2013): 1-18. <http://eudml.org/doc/275631>.

@article{Banica2013,
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.},
affiliation = {Laboratoire Analyse et probabilités (EA 2172), Déptartement de Mathématiques, Université d’Évry, 23 Bd. de France, 91037 Évry, France},
author = {Banica, Valeria},
journal = {Journées Équations aux dérivées partielles},
keywords = {Vortex filaments; selfsimilar solutions; Schrödinger equations; scattering},
language = {eng},
pages = {1-18},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Evolution by the vortex filament equation of curves with a corner},
url = {http://eudml.org/doc/275631},
year = {2013},
}

TY - JOUR
AU - Banica, Valeria
TI - Evolution by the vortex filament equation of curves with a corner
JO - Journées Équations aux dérivées partielles
PY - 2013
PB - Groupement de recherche 2434 du CNRS
SP - 1
EP - 18
AB - 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.
LA - eng
KW - Vortex filaments; selfsimilar solutions; Schrödinger equations; scattering
UR - http://eudml.org/doc/275631
ER -

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