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

Pausader, Benoit; Tzvetkov, Nikolay; Wang, Xuecheng

doi:10.1016/j.anihpc.2013.03.006

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.

Résumé

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.

MR Zbl

DOI : 10.1016/j.anihpc.2013.03.006

@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},
     pages = {315--338},
     publisher = {Elsevier},
     volume = {31},
     number = {2},
     year = {2014},
     doi = {10.1016/j.anihpc.2013.03.006},
     mrnumber = {3181672},
     zbl = {1307.35285},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2013.03.006/}
}

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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, Tome 31 (2014) no. 2, pp. 315-338. doi : 10.1016/j.anihpc.2013.03.006. http://www.numdam.org/articles/10.1016/j.anihpc.2013.03.006/

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