Global regularity for the energy-critical NLS on $ {\mathbb{S}}^{3}$

Pausader, Benoit ; Tzvetkov, Nikolay ; Wang, Xuecheng

Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014), p. 315-338 / Harvested from Numdam

Résumé

We establish global existence for the energy-critical nonlinear Schrödinger equation on $ {\mathbb{S}}^{3}$. This follows similar lines to the work on $ {\mathbb{T}}^{3}$ but requires new extinction results for linear solutions and bounds on the interaction of a Euclidean profile and a linear wave of much higher frequency that are adapted to the new geometry.

Détail

Publié le : 2014-01-01

MR 3181672 | Zbl 1307.35285

DOI : https://doi.org/10.1016/j.anihpc.2013.03.006

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