The Radial Defocusing Nonlinear Schrödinger Equation in Three Space Dimensions
Abstract
We study the defocusing nonlinear Schrödinger equation in three space dimensions. We prove that any radial solution that remains bounded in the critical Sobolev space must be global and scatter. In the energy-supercritical setting we employ a space-localized Lin-Strauss Morawetz inequality of Bourgain. In the intercritical regime we prove long-time Strichartz estimates and frequency-localized Lin-Strauss Morawetz inequalities.
Recommended Citation
J. Murphy, "The Radial Defocusing Nonlinear Schrödinger Equation in Three Space Dimensions," Communications in Partial Differential Equations, vol. 40, no. 2, pp. 265 - 308, Taylor & Francis, Feb 2015.
The definitive version is available at https://doi.org/10.1080/03605302.2014.949379
Department(s)
Mathematics and Statistics
Keywords and Phrases
Concentration-compactness; Lin-Strauss Morawetz inequality; Nonlinear Schrödinger equation; Scattering
International Standard Serial Number (ISSN)
0360-5302; 1532-4133
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2015 Taylor & Francis, All rights reserved.
Publication Date
01 Feb 2015
Comments
This work was supported in part by NSF grant DMS-1265868 (P.I. Rowan Killip).