Journal article
Energy-Critical NLS with Quadratic Potentials
Communications in partial differential equations, Vol.34(12), pp.1531-1565
12/22/2009
DOI: 10.1080/03605300903328109
Abstract
We consider the defocusing
-critical nonlinear Schrödinger equation in all dimensions (n ≥ 3) with a quadratic potential
. We show global well-posedness for radial initial data obeying ∇u
0
(x), xu
0
(x) ∈ L
2
. In view of the potential V, this is the natural energy space. In the repulsive case, we also prove scattering. We follow the approach pioneered by Bourgain and Tao in the case of no potential; indeed, we include a proof of their results that incorporates a couple of simplifications discovered while treating the problem with quadratic potential.
Details
- Title: Subtitle
- Energy-Critical NLS with Quadratic Potentials
- Creators
- Rowan Killip - University of California, Los AngelesMonica Visan - Institute for Advanced StudyXiaoyi Zhang - Chinese Academy of Sciences
- Resource Type
- Journal article
- Publication Details
- Communications in partial differential equations, Vol.34(12), pp.1531-1565
- Publisher
- Taylor & Francis Group
- DOI
- 10.1080/03605300903328109
- ISSN
- 0360-5302
- eISSN
- 1532-4133
- Language
- English
- Date published
- 12/22/2009
- Academic Unit
- Mathematics
- Record Identifier
- 9984240761402771
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