A blowup result for the periodic NLS without gauge invariance

Oh, Tadahiro

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

Oh, Tadahiro ¹

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

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

Résumé
Abstract

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.

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.

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 :

Oh, Tadahiro ¹

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

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     title = {A blowup result for the periodic {NLS} without gauge invariance},
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Oh, Tadahiro. A blowup result for the periodic NLS without gauge invariance. Comptes Rendus. Mathématique, Tome 350 (2012) no. 7-8, pp. 389-392. doi : 10.1016/j.crma.2012.04.009. http://www.numdam.org/articles/10.1016/j.crma.2012.04.009/

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