Title

The Defocusing Quintic NLS in Four Space Dimensions

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.

Department(s)

Mathematics and Statistics

Comments

B. D. was supported by NSF grant DMS-1500424. C. M. was supported by the NSFC under grant No. 11171033 and 11231006. J. M. was supported by the NSF Postdoctoral Fellowship DMS-1400706. J. Z. was partly supported by the European Research Council, ERC-2012-ADG, project number 320845: Semi-Classical Analysis of Partial Differential Equations. We thank the anonymous referee for their helpful suggestions.

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)

0294-1449

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2017 Elsevier, All rights reserved.

Publication Date

01 May 2017

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