Title

The Defocusing Energy-Supercritical NLS in Four Space Dimensions

Abstract

We consider a class of defocusing energy-supercritical nonlinear Schrödinger equations in four space dimensions. Following a concentration-compactness approach, we show that for 1 < sc < 3/2, any solution that remains bounded in the critical Sobolev space xsc(ℝ4) must be global and scatter. Key ingredients in the proof include a long-time Strichartz estimate and a frequency-localized interaction Morawetz inequality.

Department(s)

Mathematics and Statistics

Comments

C. M. was supported by the NSFC under grant Nos. 11171033 and 11231006 . J. M. was supported in part by NSF grant DMS-1001531 (P. I. Rowan Killip). J. Z. was supported by the NSFC under grant No. 11171033 . We are grateful to the anonymous referee and Rowan Killip for helpful comments.

Keywords and Phrases

Concentration-compactness; Energy-supercritical; Nonlinear Schrödinger equations; Scattering

International Standard Serial Number (ISSN)

0022-1236

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2014 Academic Press Inc., All rights reserved.

Publication Date

01 Sep 2014

Share

 
COinS