---
OA_place: repository
OA_type: green
_id: '22066'
abstract:
- lang: eng
  text: "We prove almost sure global existence and scattering for the energy-critical
    nonlinear Schrödinger equation with randomized spherically symmetric initial data
    in \U0001D43B\U0001D460⁡(ℝ4) with \r\n5/6<\U0001D460<1. We were inspired to consider
    this problem by the recent work of Dodson–Lührmann–Mendelson, which treated the
    analogous problem for the energy-critical wave equation."
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. Almost sure scattering for the energy-critical
    NLS with radial data below H1(R4). <i>Communications in Partial Differential Equations</i>.
    2019;44(1):51-71. doi:<a href="https://doi.org/10.1080/03605302.2018.1541904">10.1080/03605302.2018.1541904</a>
  apa: Killip, R., Murphy, J., &#38; Vişan, M. (2019). Almost sure scattering for
    the energy-critical NLS with radial data below H1(R4). <i>Communications in Partial
    Differential Equations</i>. Informa UK Limited. <a href="https://doi.org/10.1080/03605302.2018.1541904">https://doi.org/10.1080/03605302.2018.1541904</a>
  chicago: Killip, Rowan, Jason Murphy, and Monica Vişan. “Almost Sure Scattering
    for the Energy-Critical NLS with Radial Data below H1(R4).” <i>Communications
    in Partial Differential Equations</i>. Informa UK Limited, 2019. <a href="https://doi.org/10.1080/03605302.2018.1541904">https://doi.org/10.1080/03605302.2018.1541904</a>.
  ieee: R. Killip, J. Murphy, and M. Vişan, “Almost sure scattering for the energy-critical
    NLS with radial data below H1(R4),” <i>Communications in Partial Differential
    Equations</i>, vol. 44, no. 1. Informa UK Limited, pp. 51–71, 2019.
  ista: Killip R, Murphy J, Vişan M. 2019. Almost sure scattering for the energy-critical
    NLS with radial data below H1(R4). Communications in Partial Differential Equations.
    44(1), 51–71.
  mla: Killip, Rowan, et al. “Almost Sure Scattering for the Energy-Critical NLS with
    Radial Data below H1(R4).” <i>Communications in Partial Differential Equations</i>,
    vol. 44, no. 1, Informa UK Limited, 2019, pp. 51–71, doi:<a href="https://doi.org/10.1080/03605302.2018.1541904">10.1080/03605302.2018.1541904</a>.
  short: R. Killip, J. Murphy, M. Vişan, Communications in Partial Differential Equations
    44 (2019) 51–71.
das_tickbox: '1'
date_created: 2026-06-19T08:13:26Z
date_published: 2019-02-15T00:00:00Z
date_updated: 2026-06-30T07:16:06Z
day: '15'
doi: 10.1080/03605302.2018.1541904
extern: '1'
external_id:
  arxiv:
  - '1707.09051'
intvolume: '        44'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1707.09051
mathsc:
- 35Q55
month: '02'
oa: 1
oa_version: Preprint
page: 51-71
publication: Communications in Partial Differential Equations
publication_identifier:
  eissn:
  - 1532-4133
  issn:
  - 0360-5302
publication_status: published
publisher: Informa UK Limited
quality_controlled: '1'
scopus_import: '1'
status: public
title: Almost sure scattering for the energy-critical NLS with radial data below H1(R4)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 44
year: '2019'
...