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

Pausader, Benoit; Tzvetkov, Nikolay; Wang, Xuecheng

Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 2, pp. 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.

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