The defocusing quintic NLS in four space dimensions
Benjamin Dodson
Department of Mathematics, Johns Hopkins University, Baltimore, MD, USAChangxing Miao
Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088, ChinaJason Murphy
Department of Mathematics, University of California, Berkeley, USAJiqiang Zheng
Université Nice Sophia-Antipolis, 06108 Nice Cedex 02, France
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.
Cite this article
Benjamin Dodson, Changxing Miao, Jason Murphy, Jiqiang Zheng, The defocusing quintic NLS in four space dimensions. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 3, pp. 759–787
DOI 10.1016/J.ANIHPC.2016.05.004