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 Ḣxsc(ℝ4) must be global and scatter. Key ingredients in the proof include a long-time Strichartz estimate and a frequency-localized interaction Morawetz inequality.
Recommended Citation
C. Miao et al., "The Defocusing Energy-Supercritical NLS in Four Space Dimensions," Journal of Functional Analysis, vol. 267, no. 6, pp. 1662 - 1724, Academic Press Inc., Sep 2014.
The definitive version is available at https://doi.org/10.1016/j.jfa.2014.06.016
Department(s)
Mathematics and Statistics
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
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.