---
OA_place: repository
OA_type: green
_id: '22084'
abstract:
- lang: eng
  text: 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.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Rowan
  full_name: Killip, Rowan
  last_name: Killip
- first_name: Jason
  full_name: Murphy, Jason
  last_name: Murphy
- first_name: Monica
  full_name: Visan, Monica
  id: 056daca0-b8d1-11f0-964f-f91054abf8ca
  last_name: Visan
citation:
  ama: 'Killip R, Murphy J, Vişan M. Scattering for the cubic-quintic NLS: Crossing
    the virial threshold. <i>SIAM Journal on Mathematical Analysis</i>. 2021;53(5):5803-5812.
    doi:<a href="https://doi.org/10.1137/20m1381824">10.1137/20m1381824</a>'
  apa: 'Killip, R., Murphy, J., &#38; Vişan, M. (2021). Scattering for the cubic-quintic
    NLS: Crossing the virial threshold. <i>SIAM Journal on Mathematical Analysis</i>.
    Society for Industrial &#38; Applied Mathematics. <a href="https://doi.org/10.1137/20m1381824">https://doi.org/10.1137/20m1381824</a>'
  chicago: 'Killip, Rowan, Jason Murphy, and Monica Vişan. “Scattering for the Cubic-Quintic
    NLS: Crossing the Virial Threshold.” <i>SIAM Journal on Mathematical Analysis</i>.
    Society for Industrial &#38; Applied Mathematics, 2021. <a href="https://doi.org/10.1137/20m1381824">https://doi.org/10.1137/20m1381824</a>.'
  ieee: 'R. Killip, J. Murphy, and M. Vişan, “Scattering for the cubic-quintic NLS:
    Crossing the virial threshold,” <i>SIAM Journal on Mathematical Analysis</i>,
    vol. 53, no. 5. Society for Industrial &#38; Applied Mathematics, pp. 5803–5812,
    2021.'
  ista: '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.'
  mla: 'Killip, Rowan, et al. “Scattering for the Cubic-Quintic NLS: Crossing the
    Virial Threshold.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 53, no.
    5, Society for Industrial &#38; Applied Mathematics, 2021, pp. 5803–12, doi:<a
    href="https://doi.org/10.1137/20m1381824">10.1137/20m1381824</a>.'
  short: R. Killip, J. Murphy, M. Vişan, SIAM Journal on Mathematical Analysis 53
    (2021) 5803–5812.
das_tickbox: '1'
date_created: 2026-06-19T08:28:23Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2026-07-01T07:37:46Z
day: '01'
doi: 10.1137/20m1381824
extern: '1'
external_id:
  arxiv:
  - '2007.07406'
fulldoi: https://doi.org/10.1137/20m1381824
intvolume: '        53'
issue: '5'
keyword:
- NLS
- scattering
- viral
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2007.07406
mathsc:
- 35Q55
month: '01'
oa: 1
oa_version: Preprint
page: 5803-5812
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
  eissn:
  - 1095-7154
  issn:
  - 0036-1410
publication_status: published
publisher: Society for Industrial & Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Scattering for the cubic-quintic NLS: Crossing the virial threshold'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 53
year: '2021'
...