A blowup result for the periodic NLS without gauge invariance

Tadahiro Oh

doi:10.1016/j.crma.2012.04.009

Partial Differential Equations

A blowup result for the periodic NLS without gauge invariance
[Un résultat dʼexplosion pour lʼéquation de Schrödinger non linéaire sans invariance de gauge dans le cas périodique]

Présenté par : the Editorial Board

Tadahiro Oh ¹

¹ Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544-1000, USA

Comptes Rendus. Mathématique, Volume 350 (2012) no. 7-8, pp. 389-392.

Abstract (VO)
Résumé

In this Note, we prove a finite-time blowup result for the periodic nonlinear Schrödinger equation on $T^{d}$ with nonlinearity ${| u |}^{p}$ for $p > 1$ . In particular, our blowup result holds above the Strauss exponent. This is in contrast with the non-periodic setting, where global existence for small data is known above the Strauss exponent.

Dans cette Note, nous démontrons un résultat dʼexplosion en temps fini pour lʼéquation de Schrödinger non linéaire sur le tore $T^{d}$ avec une non linéarité du type ${| u |}^{p}$ , $p > 1$ . En particulier, notre résultat dʼexplosion est vrai pour des puissances p plus grandes que lʼexposant de Strauss. Cette situation est contraire au cas non périodique où lʼon connaît que pour p supérieur à lʼexposant de Strauss, le problème de Cauchy est globalement bien posé.

Reçu le : 2012-02-22
Accepté le : 2012-04-10
Publié le : 2012-04-01

DOI : 10.1016/j.crma.2012.04.009

Affiliations des auteurs :

Tadahiro Oh ¹

¹ Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544-1000, USA

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Tadahiro Oh. A blowup result for the periodic NLS without gauge invariance. Comptes Rendus. Mathématique, Volume 350 (2012) no. 7-8, pp. 389-392. doi : 10.1016/j.crma.2012.04.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.04.009/

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