Scattering for the Cubic-Quintic Nls: Crossing the Virial Threshold

Author

Rowan Killip
Jason Murphy, Missouri University of Science and TechnologyFollow
Monica Visan

Abstract

We consider the nonlinear Schrödinger equation in three space dimensions with combined focusing cubic and defocusing quintic nonlinearity. This problem was considered previously by Killip et al. [Arch. Ration. Mech. Anal., 225 (2017), pp. 469–548], who proved scattering for the whole region of the mass/energy plane where the virial quantity is guaranteed to be positive. In this paper, we prove scattering in a slightly larger region where, in particular, the virial quantity is no longer guaranteed to be sign definite.

Recommended Citation

R. Killip et al., "Scattering for the Cubic-Quintic Nls: Crossing the Virial Threshold," SIAM Journal on Mathematical Analysis, vol. 53, no. 5, pp. 5803 - 5812, Society for Industrial and Applied Mathematics, Jan 2021.

The definitive version is available at https://doi.org/10.1137/20M1381824

Department(s)

Mathematics and Statistics

Comments

National Science Foundation, Grant DMS-1763074

Keywords and Phrases

NLS; scattering; virial

International Standard Serial Number (ISSN)

1095-7154; 0036-1410

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 2024 Society for Industrial and Applied Mathematics, All rights reserved.

Publication Date

01 Jan 2021