The Focusing Cubic NLS with Inverse-Square Potential in Three Space Dimensions
Abstract
We consider the focusing cubic nonlinear Schrödinger equation with inverse-square potential in three space dimensions. We identify a sharp threshold between scattering and blowup, establishing a result analogous to that of Duyckaerts, Holmer, and Roudenko for the standard focusing cubic NLS [7, 11]. We also prove failure of uniform space-time bounds at the threshold.
Recommended Citation
R. Killip et al., "The Focusing Cubic NLS with Inverse-Square Potential in Three Space Dimensions," Differential and Integral Equations, vol. 30, no. 2019-03-04, pp. 161 - 206, Khayyam Publishing, Mar 2017.
Department(s)
Mathematics and Statistics
International Standard Serial Number (ISSN)
0893-4983
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2017 Khayyam Publishing, All rights reserved.
Publication Date
01 Mar 2017
Comments
R. K. was supported by the NSF grant DMS-1265868. J. M. was supported by the NSF Postdoctoral Fellowship DMS-1400706. M. V. was supported by the NSF grant DMS-1500707. J. Z. was partly supported by the European Research Council, ERC-2012-ADG, project number 320845: Semi-Classical Analysis of Partial Differential Equations. The work on this project was supported in part by NSF grant DMS-1440140, while the authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Fall 2015 semester. We thank the anonymous referee for their careful reading of the manuscript.