Title

Intercritical NLS: Critical Ḣˢ-Bounds Imply Scattering

Abstract

We consider a class of power-type nonlinear Schrödinger equations for which the power of the nonlinearity lies between the mass-and energy-critical exponents. Following the concentration-compactness approach, we prove that if a solution u is bounded in the critical Sobolev space throughout its lifespan, that is, u ∈ Lt∞ Ḣxsc, then u is global and scatters.

Department(s)

Mathematics and Statistics

Comments

This work was supported in part by NSF grant DMS-1001531 (P. I. Rowan Killip).

Keywords and Phrases

Dinger equation; Intercritical; Life span; NLS; Nonlinear equations; Scattering; Concentration compactness; Intercritical; NLS; Scattering

International Standard Serial Number (ISSN)

0036-1410

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2014 Society for Industrial and Applied Mathematics, All rights reserved.

Publication Date

01 Jan 2014

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