Intercritical NLS: Critical Ḣˢ-Bounds Imply Scattering

Author

Jason Murphy, Missouri University of Science and TechnologyFollow

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 ∈ L_t∞ Ḣ_x^sc, then u is global and scatters.

Recommended Citation

J. Murphy, "Intercritical NLS: Critical Ḣˢ-Bounds Imply Scattering," SIAM Journal on Mathematical Analysis, vol. 46, no. 1, pp. 939 - 997, Society for Industrial and Applied Mathematics (SIAM), Jan 2014.

The definitive version is available at https://doi.org/10.1137/120898280

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 (SIAM), All rights reserved.

Publication Date

01 Jan 2014