Geodesic
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

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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.

DOI : 10.1016/j.anihpc.2016.05.004
Keywords: Nonlinear Schrödinger equation, Concentration compactness, Scattering, Interaction Morawetz inequality 
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     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},
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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

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