The Defocusing Quintic NLS in Four Space Dimensions
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.
B. Dodson et al., "The Defocusing Quintic NLS in Four Space Dimensions," Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, vol. 34, no. 3, pp. 759-787, Elsevier, May 2017.
The definitive version is available at https://doi.org/10.1016/j.anihpc.2016.05.004
Mathematics and Statistics
Keywords and Phrases
Nonlinear equations; Scattering; Defocusing; Dinger equation; Four dimensions; Interaction Morawetz inequality; Localized interaction; Logarithmic failure; Quintic; Space dimensions; Sobolev spaces; Concentration compactness; Interaction Morawetz inequality; Nonlinear Schrödinger equation
International Standard Serial Number (ISSN)
Article - Journal
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01 May 2017