Journal article
Minimal-mass blowup solutions of the mass-critical NLS
Forum mathematicum, Vol.20(5), pp.881-919
10/2008
DOI: 10.1515/FORUM.2008.042
Abstract
We consider the minimal mass m 0 required for solutions to the mass-critical nonlinear Schrödinger (NLS) equation iut + Δu = μ|u|4/d u to blow up. If m 0 is finite, we show that there exists a minimal-mass solution blowing up (in the sense of an infinite spacetime norm) in both time directions, whose orbit in is compact after quotienting out by the symmetries of the equation. A similar result is obtained for spherically symmetric solutions. Similar results were previously obtained by Keraani, [Keraani S.: On the blow-up phenomenon of the critical nonlinear Schrödinger equation. J. Funct. Anal. 235 (2006), 171–192], in dimensions 1, 2 and Begout and Vargas, [Begout P., Vargas A.: Mass concentration phenomena for the L 2-critical nonlinear Schrödinger equation, preprint], in dimensions d ≥ 3 for the mass-critical NLS and by Kenig and Merle, [Kenig C., Merle F.: Global well-posedness, scattering, and blowup for the energy-critical, focusing, non-linear Schrödinger equation in the radial case, preprint], in the energy-critical case. In a subsequent paper we shall use this compactness result to establish global existence and scattering in for the defocusing NLS in three and higher dimensions with spherically symmetric data.
Details
- Title: Subtitle
- Minimal-mass blowup solutions of the mass-critical NLS
- Creators
- Terence Tao - Department of Mathematics, UCLA, Los Angeles CA 90095-1555. tao@math.ucla.eduMonica Visan - E-mail: mvisan@ias.eduXiaoyi Zhang - Academy of Mathematics and System Sciences, Chinese Academy of Sciences. zh.xiaoyi@gmail.com
- Resource Type
- Journal article
- Publication Details
- Forum mathematicum, Vol.20(5), pp.881-919
- Publisher
- Walter de Gruyter GmbH & Co. KG
- DOI
- 10.1515/FORUM.2008.042
- ISSN
- 0933-7741
- eISSN
- 1435-5337
- Language
- English
- Date published
- 10/2008
- Academic Unit
- Mathematics
- Record Identifier
- 9984240775702771
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