Title

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.

Department(s)

Mathematics and Statistics

Comments

This work was supported in part by NSF grant DMS-1265868 (P.I. Rowan Killip).

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

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