Global regularity for the energy-critical NLS on ${𝕊}^{3}$
Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 2, p. 315-338

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.

@article{AIHPC_2014__31_2_315_0,
author = {Pausader, Benoit and Tzvetkov, Nikolay and Wang, Xuecheng},
title = {Global regularity for the energy-critical NLS on ${\mathbb{S}}^{3}$},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {31},
number = {2},
year = {2014},
pages = {315-338},
doi = {10.1016/j.anihpc.2013.03.006},
zbl = {1307.35285},
mrnumber = {3181672},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2014__31_2_315_0}
}

Pausader, Benoit; Tzvetkov, Nikolay; Wang, Xuecheng. Global regularity for the energy-critical NLS on ${\mathbb{S}}^{3}$. Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 2, pp. 315-338. doi : 10.1016/j.anihpc.2013.03.006. http://www.numdam.org/item/AIHPC_2014__31_2_315_0/

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