Comptes Rendus
no. 7-8
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 Oh1
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.

Dans cette Note, nous démontrons un résultat dʼexplosion en temps fini pour lʼéquation de Schrödinger non linéaire sur le tore Td 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.

In this Note, we prove a finite-time blowup result for the periodic nonlinear Schrödinger equation on Td 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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.04.009

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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