Scattering for the cubic-quintic NLS: Crossing the virial threshold
Killip R, Murphy J, Vişan M. 2021. Scattering for the cubic-quintic NLS: Crossing the virial threshold. SIAM Journal on Mathematical Analysis. 53(5), 5803–5812.
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Author
Killip, Rowan;
Murphy, Jason;
Vişan, MonicaISTA
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.
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Mathematics Subject Classification
Publishing Year
Date Published
2021-01-01
Journal Title
SIAM Journal on Mathematical Analysis
Publisher
Society for Industrial & Applied Mathematics
Volume
53
Issue
5
Page
5803-5812
ISSN
eISSN
IST-REx-ID
Cite this
Killip R, Murphy J, Vişan M. Scattering for the cubic-quintic NLS: Crossing the virial threshold. SIAM Journal on Mathematical Analysis. 2021;53(5):5803-5812. doi:10.1137/20m1381824
Killip, R., Murphy, J., & Vişan, M. (2021). Scattering for the cubic-quintic NLS: Crossing the virial threshold. SIAM Journal on Mathematical Analysis. Society for Industrial & Applied Mathematics. https://doi.org/10.1137/20m1381824
Killip, Rowan, Jason Murphy, and Monica Vişan. “Scattering for the Cubic-Quintic NLS: Crossing the Virial Threshold.” SIAM Journal on Mathematical Analysis. Society for Industrial & Applied Mathematics, 2021. https://doi.org/10.1137/20m1381824.
R. Killip, J. Murphy, and M. Vişan, “Scattering for the cubic-quintic NLS: Crossing the virial threshold,” SIAM Journal on Mathematical Analysis, vol. 53, no. 5. Society for Industrial & Applied Mathematics, pp. 5803–5812, 2021.
Killip R, Murphy J, Vişan M. 2021. Scattering for the cubic-quintic NLS: Crossing the virial threshold. SIAM Journal on Mathematical Analysis. 53(5), 5803–5812.
Killip, Rowan, et al. “Scattering for the Cubic-Quintic NLS: Crossing the Virial Threshold.” SIAM Journal on Mathematical Analysis, vol. 53, no. 5, Society for Industrial & Applied Mathematics, 2021, pp. 5803–12, doi:10.1137/20m1381824.
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