Partial Differential Equations
Strichartz estimates for the periodic non-elliptic Schrödinger equation

Presented by: Jean Bourgain

Godet, Nicolas1; Tzvetkov, Nikolay1
1 CNRS & Laboratoire de Mathématiques (UMR 8088), Université de Cergy-Pontoise, F-95000 Cergy-Pontoise, France
Comptes Rendus. Mathématique, Volume 350 (2012) no. 21-22, pp. 955-958.

The purpose of this Note is to prove sharp Strichartz estimates with derivative losses for the non-elliptic Schrödinger equation posed on the 2-dimensional torus.

Le but de cette Note est de démontrer des estimations de Strichartz optimales avec pertes de dérivées pour lʼéquation de Schrödinger non-elliptique posée sur le tore de dimension 2.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2012.10.029
Godet, Nicolas 1; Tzvetkov, Nikolay 1

1 CNRS & Laboratoire de Mathématiques (UMR 8088), Université de Cergy-Pontoise, F-95000 Cergy-Pontoise, France 
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Godet, Nicolas; Tzvetkov, Nikolay. Strichartz estimates for the periodic non-elliptic Schrödinger equation. Comptes Rendus. Mathématique, Volume 350 (2012) no. 21-22, pp. 955-958. doi : 10.1016/j.crma.2012.10.029. https://www.numdam.org/articles/10.1016/j.crma.2012.10.029/

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[3] Burq, N.; Gérard, P.; Tzvetkov, N. Bilinear eigenfunction estimates and the nonlinear Schrödinger equation on surfaces, Invent. Math., Volume 159 (2005), pp. 187-223

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[5] Y. Wang, Periodic cubic hyperbolic Schrödinger equation on T2, preprint.

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