Title

The Defocusing Ḣ¹ᐟ²-Critical NLS in High Dimensions

Abstract

We consider the defocusing Ḣ1/2-critical nonlinear Schrödinger equation in dimensions d ≥ 4. In the spirit of Kenig and Merle [10], we combine a concentration-compactness approach with the Lin-Strauss Morawetz inequality to prove that if a solution u is bounded in Ḣ1/2 throughout its lifespan, then u is global and scatters.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Concentration-compactness; Ḣ1/2-critical; Lin-Strauss Morawetz inequality; Nonlinear Schrödinger equation; Scattering

International Standard Serial Number (ISSN)

1078-0947; 1553-5231

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2014 American Institute of Mathematical Sciences (AIMS), All rights reserved.

Publication Date

01 Feb 2014

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