Article

Access to the text (HTML) Access to the text (HTML)
PDF Access to the PDF text
Advertising


Access to the full text of this article requires a subscription.
  • If you are a subscriber, please sign in 'My Account' at the top right of the screen.

  • If you want to subscribe to this journal, see our rates

  • You can purchase this item in Pay Per ViewPay per View - FAQ : 30,00 € Taxes included to order
    Pages Iconography Videos Other
    6 0 0 0


Comptes Rendus Mathématique
Volume 342, n° 11
pages 837-842 (juin 2006)
Doi : 10.1016/j.crma.2006.04.008
Received : 30 Mars 2006 ; 
Dynamics of multiple degree Ginzburg-Landau vortices
Dynamique des tourbillons de vorticité de degré multiple pour lʼéquation de Ginzburg-Landau
 

Fabrice Bethuel a, b , Giandomenico Orlandi c , Didier Smets a
a Laboratoire Jacques-Louis Lions, université de Paris 6, 4, place Jussieu, BC 187, 75252 Paris cedex 05, France 
b Institut Universitaire de France 
c Dipartimento di Informatica, Università di Verona, Strada le Grazie, 37134 Verona, Italy 

Abstract

For the two-dimensional complex parabolic Ginzburg-Landau equation we prove that, asymptotically, vortices evolve according to a simple ordinary differential equation, which is a gradient flow of the Kirchhoff-Onsager functional. This convergence holds except for a finite number of times, corresponding to vortex collisions and splittings, which we describe carefully. The only assumption is a natural energy bound on the initial data. To cite this article: F. Bethuel et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).

The full text of this article is available in PDF format.
Résumé

Nous montrons, pour lʼéquation de Ginzburg-Landau parabolique complexe en dimension deux, quʼasymptotiquement les tourbillons se déplacent suivant un flot gradient pour la fonctionnelle de Kirchhoff-Onsager. Cette convergence a lieu en dehors dʼun nombre fini dʼinstants qui correspondent aux éclatements et aux collisions des tourbillons, que nous décrivons en détail. Notre unique hypothèse sur les données initiales est une borne dʼénergie. Pour citer cet article : F. Bethuel et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).

The full text of this article is available in PDF format.


© 2006  Académie des sciences@@#104156@@
EM-CONSULTE.COM is registrered at the CNIL, déclaration n° 1286925.
As per the Law relating to information storage and personal integrity, you have the right to oppose (art 26 of that law), access (art 34 of that law) and rectify (art 36 of that law) your personal data. You may thus request that your data, should it be inaccurate, incomplete, unclear, outdated, not be used or stored, be corrected, clarified, updated or deleted.
Personal information regarding our website's visitors, including their identity, is confidential.
The owners of this website hereby guarantee to respect the legal confidentiality conditions, applicable in France, and not to disclose this data to third parties.
Close
Article Outline
You can move this window by clicking on the headline
@@#110903@@