Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773501 | Annales de l'Institut Henri Poincare (C) Non Linear Analysis | 2017 | 29 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Benjamin Dodson, Changxing Miao, Jason Murphy, Jiqiang Zheng,