Strichartz estimates for the periodic non-elliptic Schrödinger equation

Nicolas Godet; Nikolay Tzvetkov

doi:10.1016/j.crma.2012.10.029

Partial Differential Equations

Strichartz estimates for the periodic non-elliptic Schrödinger equation

Presented by: Jean Bourgain

Nicolas Godet ¹; Nikolay Tzvetkov ¹

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.

Abstract
Résumé

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: 2012-06-28
Accepted: 2012-10-29
Published online: 2012-11-01

DOI: 10.1016/j.crma.2012.10.029

Author's affiliations:

Nicolas Godet ¹; Nikolay Tzvetkov ¹

¹ CNRS & Laboratoire de Mathématiques (UMR 8088), Université de Cergy-Pontoise, F-95000 Cergy-Pontoise, France

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     author = {Nicolas Godet and Nikolay Tzvetkov},
     title = {Strichartz estimates for the periodic non-elliptic {Schr\"odinger} equation},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {955--958},
     publisher = {Elsevier},
     volume = {350},
     number = {21-22},
     year = {2012},
     doi = {10.1016/j.crma.2012.10.029},
     language = {en},
}

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Nicolas Godet; Nikolay Tzvetkov. 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://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.10.029/

References
Cited by

[1] J. Bourgain Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations, Geom. Funct. Anal., Volume 3 (1993), pp. 107-156

[2] N. Burq; P. Gérard; N. Tzvetkov Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds, Amer. J. Math., Volume 126 (2004), pp. 569-605

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

[4] D. Salort The Schrödinger equation type with a nonelliptic operator, Comm. Partial Differential Equations, Volume 32 (2007) no. 1–3, pp. 209-228

[5] Y. Wang, Periodic cubic hyperbolic Schrödinger equation on $T^{2}$ , preprint.

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