JournalsaihpcVol. 34, No. 3pp. 759–787

The defocusing quintic NLS in four space dimensions

  • Benjamin Dodson

    Department of Mathematics, Johns Hopkins University, Baltimore, MD, USA

  • Changxing Miao

    Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088, China

  • Jason Murphy

    Department of Mathematics, University of California, Berkeley, USA

  • Jiqiang Zheng

    Université Nice Sophia-Antipolis, 06108 Nice Cedex 02, France
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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