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.
Recommended Citation
J. Lu et al., "Scattering in H¹ for the Intercritical NLS with an Inverse-Square Potential," Journal of Differential Equations, vol. 264, no. 5, pp. 3174 - 3211, Academic Press Inc., Mar 2018.
The definitive version is available at https://doi.org/10.1016/j.jde.2017.11.015
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.
Publication Date
01 Mar 2018
