Journal article
Global well-posedness and scattering for the defocusing mass-critical nonlinear Schrödinger equation for radial data in high dimensions
Duke mathematical journal, Vol.140(1), pp.165-202
10/01/2007
DOI: 10.1215/S0012-7094-07-14015-8
Abstract
We establish global well-posedness and scattering for solutions to the defocusing mass-critical (pseudoconformal) nonlinear Schrödinger equation iu t + Δ u = | u | 4 / n u for large, spherically symmetric, L x 2 ( R n ) initial data in dimensions n ≥ 3 . After using the concentration-compactness reductions in [32] to reduce to eliminating blow-up solutions that are almost periodic modulo scaling, we obtain a frequency-localized Morawetz estimate and exclude a mass evacuation scenario (somewhat analogously to [10], [23], [36]) in order to conclude the argument
Details
- Title: Subtitle
- Global well-posedness and scattering for the defocusing mass-critical nonlinear Schrödinger equation for radial data in high dimensions
- Creators
- Terence Tao - University of California, BerkeleyMonica Visan - Institute for Advanced StudyXiaoyi Zhang - Chinese Academy of Sciences
- Resource Type
- Journal article
- Publication Details
- Duke mathematical journal, Vol.140(1), pp.165-202
- DOI
- 10.1215/S0012-7094-07-14015-8
- ISSN
- 0012-7094
- eISSN
- 1547-7398
- Publisher
- DUKE University Press
- Language
- English
- Date published
- 10/01/2007
- Academic Unit
- Mathematics
- Record Identifier
- 9984240761902771
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