no. 7-8
Partial Differential Equations
Non-existence for travelling waves with small energy for the Gross–Pitaevskii equation in dimension N⩾3
[Non existence pour les ondes progressives d'énergie petite pour l'équation de Gross–Pitaevskii en dimension N⩾3]

Présenté par : Haïm Brezis

de Laire, André1
1 UPMC Université Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France
Comptes Rendus. Mathématique, Tome 347 (2009) no. 7-8, pp. 375-380.

On démontre que l'énergie de Ginzburg–Landau des ondes progressives non constantes de l'équation de Gross–Pitaevskii est bornée inférieurement par une constante positive qui ne dépend que de la dimension, pour toute dimension supérieure ou égale à trois. En particulier, on en déduit qu'il n'existe pas d'onde progressive non constante d'énergie petite.

We prove that the Ginzburg–Landau energy of non-constant travelling waves of the Gross–Pitaevskii equation has a lower positive bound, depending only on the dimension, in any dimension larger or equal to three. In particular, we conclude that there are no non-constant travelling waves with small energy.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.02.006
de Laire, André 1

1 UPMC Université Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France 
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de Laire, André. Non-existence for travelling waves with small energy for the Gross–Pitaevskii equation in dimension $ N⩾3$. Comptes Rendus. Mathématique, Tome 347 (2009) no. 7-8, pp. 375-380. doi : 10.1016/j.crma.2009.02.006. http://www.numdam.org/articles/10.1016/j.crma.2009.02.006/

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