We consider the defocusing quintic nonlinear Schrödinger equation in four space dimensions. We prove that any solution that remains bounded in the critical Sobolev space must be global and scatter. We employ a space-localized interaction Morawetz inequality, the proof of which requires us to overcome the logarithmic failure in the double Duhamel argument in four dimensions.
@article{AIHPC_2017__34_3_759_0, author = {Dodson, Benjamin and Miao, Changxing and Murphy, Jason and Zheng, Jiqiang}, title = {The defocusing quintic {NLS} in four space dimensions}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {759--787}, publisher = {Elsevier}, volume = {34}, number = {3}, year = {2017}, doi = {10.1016/j.anihpc.2016.05.004}, zbl = {1367.35154}, mrnumber = {3633744}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2016.05.004/} }
TY - JOUR AU - Dodson, Benjamin AU - Miao, Changxing AU - Murphy, Jason AU - Zheng, Jiqiang TI - The defocusing quintic NLS in four space dimensions JO - Annales de l'I.H.P. Analyse non linéaire PY - 2017 SP - 759 EP - 787 VL - 34 IS - 3 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2016.05.004/ DO - 10.1016/j.anihpc.2016.05.004 LA - en ID - AIHPC_2017__34_3_759_0 ER -
%0 Journal Article %A Dodson, Benjamin %A Miao, Changxing %A Murphy, Jason %A Zheng, Jiqiang %T The defocusing quintic NLS in four space dimensions %J Annales de l'I.H.P. Analyse non linéaire %D 2017 %P 759-787 %V 34 %N 3 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2016.05.004/ %R 10.1016/j.anihpc.2016.05.004 %G en %F AIHPC_2017__34_3_759_0
Dodson, Benjamin; Miao, Changxing; Murphy, Jason; Zheng, Jiqiang. The defocusing quintic NLS in four space dimensions. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 3, pp. 759-787. doi : 10.1016/j.anihpc.2016.05.004. http://archive.numdam.org/articles/10.1016/j.anihpc.2016.05.004/
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