Threshold scattering for the 2D radial cubic-quintic NLS. Issue 11 (2nd November 2021)

• Record Type: Journal Article
• Authors: Murphy, Jason
• Is Part Of: Communications in partial differential equations. Volume 46:Issue 11(2021)
• Page Start: 2213
• Page End: 2234
• Publication Date: 2021-11-02
• Subjects: Cubic-quintic NLS -- scattering -- scattering threshold; Differential equations, Partial -- Periodicals; 515.353
• DOI: 10.1080/03605302.2021.1928701
• Languages: English
• ISSNs: 0360-5302

Abstract

Abstract: We consider the cubic-quintic nonlinear Schrödinger equation in two space dimensions. For this model, X. Cheng established scattering for H 1 data with mass strictly below that of the ground state for the cubic NLS. Subsequently, R. Carles and C. Sparber utilized the pseudoconformal energy estimate to obtain scattering at the sharp threshold for data belonging to a weighted Sobolev space. In this work, we remove the weighted assumption and establish scattering at the threshold for radial data in H 1 .