We establish global existence for the energy-critical nonlinear Schrödinger equation on . This follows similar lines to the work on 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}, 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/} }
TY - JOUR AU - Pausader, Benoit AU - Tzvetkov, Nikolay AU - Wang, Xuecheng TI - Global regularity for the energy-critical NLS on $ {\mathbb{S}}^{3}$ JO - Annales de l'I.H.P. Analyse non linéaire PY - 2014 SP - 315 EP - 338 VL - 31 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2013.03.006/ DO - 10.1016/j.anihpc.2013.03.006 LA - en ID - AIHPC_2014__31_2_315_0 ER -
%0 Journal Article %A Pausader, Benoit %A Tzvetkov, Nikolay %A Wang, Xuecheng %T Global regularity for the energy-critical NLS on $ {\mathbb{S}}^{3}$ %J Annales de l'I.H.P. Analyse non linéaire %D 2014 %P 315-338 %V 31 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2013.03.006/ %R 10.1016/j.anihpc.2013.03.006 %G en %F 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/articles/10.1016/j.anihpc.2013.03.006/
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