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

Xuecheng Wang; Benoit Pausader; Nikolay Tzvetkov

doi:10.1016/j.anihpc.2013.03.006

JournalsaihpcVol. 31, No. 2pp. 315–338

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

Xuecheng Wang
Princeton University, United States
Benoit Pausader
Université Paris 13, Sorbonne Paris Cité, LAGA, CNRS (UMR 7539), F-93430 Villetaneuse, France
Nikolay Tzvetkov
Université Cergy-Pontoise, UMR CNRS 8088, F-95000 Cergy-Pontoise, France

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

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Abstract

We establish global existence for the energy-critical nonlinear Schrödinger equation on $S^{3}$ . This follows similar lines to the work on $T^{3}$ 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.

Cite this article

Xuecheng Wang, Benoit Pausader, Nikolay Tzvetkov, Global regularity for the energy-critical NLS on $S^{3}$ . Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 2, pp. 315–338

DOI 10.1016/J.ANIHPC.2013.03.006