A remark on global well-posedness of the derivative nonlinear Schrödinger equation on the circle

Razvan Mosincat; Tadahiro Oh

doi:10.1016/j.crma.2015.06.015

Partial differential equations

A remark on global well-posedness of the derivative nonlinear Schrödinger equation on the circle
[Une remarque sur le caractère globalement bien posé de l'équation de Schrödinger non linéaire avec dérivée sur le cercle]

Présenté par : Haïm Brézis

Razvan Mosincat ^1,² ; Tadahiro Oh ^1,²

¹ School of Mathematics, The University of Edinburgh, James Clerk Maxwell Building, The King's Buildings, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom
² The Maxwell Institute for the Mathematical Sciences, James Clerk Maxwell Building, The King's Buildings, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom

Comptes Rendus. Mathématique, Volume 353 (2015) no. 9, pp. 837-841.

Résumé
Abstract

On considère dans cette note l'équation de Schrödinger avec dérivée sur le cercle. En particulier, en adaptant l'argument récent de Wu au cas periodique, on prouve que cette équation est globalement bien posée dans $H^{1} (T)$ , pourvu que la masse soit inférieure à 4π. En outre, ce seuil pour la masse est indépendant des périodes spatiales.

In this note, we consider the derivative nonlinear Schrödinger equation on the circle. In particular, by adapting Wu's recent argument to the periodic setting, we prove its global well-posedness in $H^{1} (T)$ , provided that the mass is less than 4π. Moreover, this mass threshold is independent of spatial periods.

Reçu le : 2014-11-12
Accepté le : 2015-06-12
Publié le : 2015-07-21

DOI : 10.1016/j.crma.2015.06.015

Affiliations des auteurs :

Razvan Mosincat ^{1, 2} ; Tadahiro Oh ^{1, 2}

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     title = {A remark on global well-posedness of the derivative nonlinear {Schr\"odinger} equation on the circle},
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Razvan Mosincat; Tadahiro Oh. A remark on global well-posedness of the derivative nonlinear Schrödinger equation on the circle. Comptes Rendus. Mathématique, Volume 353 (2015) no. 9, pp. 837-841. doi : 10.1016/j.crma.2015.06.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.06.015/

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