Vortex motion and phase-vortex interaction in dissipative Ginzburg-Landau dynamics
Journées équations aux dérivées partielles (2004), article no. 10, 12 p.

We discuss the asymptotics of the parabolic Ginzburg-Landau equation in dimension N2. Our only asumption on the initial datum is a natural energy bound. Compared to the case of “well-prepared” initial datum, this induces possible new energy modes which we analyze, and in particular their mutual interaction. The two dimensional case is qualitatively different and requires a separate treatment.

Nous étudions l’équation de Ginzburg-Landau parabolique sur l’espace tout entier, plus particulièrement lorsqu’une des échelles caractéristiques tend vers zéro. Notre seule hypothèse sur la donnée initiale est une borne naturelle sur l’énergie. En comparaison avec le cas des données préparées, notre hypothèse laisse place à de nouveaux phénomènes, en particulier la présence de différents modes pour l’énergie, dont nous étudions l’interaction. Le cas de la dimension 2 d’espace est qualitativement différent et requiert une analyse séparée.

@article{JEDP_2004____A10_0,
     author = {Bethuel, F. and Orlandi, G. and Smets, D.},
     title = {Vortex motion and phase-vortex interaction in dissipative Ginzburg-Landau dynamics},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     publisher = {Groupement de recherche 2434 du CNRS},
     year = {2004},
     doi = {10.5802/jedp.10},
     mrnumber = {2135365},
     zbl = {1067.35031},
     language = {en},
     url = {http://www.numdam.org/item/JEDP_2004____A10_0}
}
Bethuel, F.; Orlandi, G.; Smets, D. Vortex motion and phase-vortex interaction in dissipative Ginzburg-Landau dynamics. Journées équations aux dérivées partielles (2004), article  no. 10, 12 p. doi : 10.5802/jedp.10. http://www.numdam.org/item/JEDP_2004____A10_0/

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