Title

Scattering in H¹ for the Intercritical NLS with an Inverse-Square Potential

Abstract

We study the nonlinear Schrödinger equation with an inverse-square potential in dimensions 3 ≤ d ≤ 6. We consider both focusing and defocusing nonlinearities in the mass-supercritical and energy-subcritical regime. In the focusing case, we prove a scattering/blowup dichotomy below the ground state. In the defocusing case, we prove scattering in H1 for arbitrary data.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Inverse-square potential; Nonlinear Schrödinger equation; Scattering

International Standard Serial Number (ISSN)

0022-0396

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2018 Academic Press Inc., All rights reserved.

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