---
OA_place: repository
OA_type: green
_id: '22090'
abstract:
- lang: eng
  text: "We establish global well-posedness and scattering for solutions to the mass-critical
    nonlinear Schrödinger equation iu \r\nt\r\n​\r\n +Δu=±∣u∣ \r\n2\r\n u for large
    spherically symmetric L \r\nx\r\n2\r\n​\r\n (R \r\n2\r\n ) initial data; in the
    focusing case we require, of course, that the mass is strictly less than that
    of the ground state. As a consequence, we deduce that in the focusing case, any
    spherically symmetric blowup solution must concentrate at least the mass of the
    ground state at the blowup time.\r\n\r\nWe also establish some partial results
    towards the analogous claims in other dimensions and without the assumption of
    spherical symmetry."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Rowan
  full_name: Killip, Rowan
  last_name: Killip
- first_name: Terence
  full_name: Tao, Terence
  last_name: Tao
- first_name: Monica
  full_name: Visan, Monica
  id: 056daca0-b8d1-11f0-964f-f91054abf8ca
  last_name: Visan
citation:
  ama: Killip R, Tao T, Vişan M. The cubic nonlinear Schrödinger equation in two dimensions
    with radial data. <i>Journal of the European Mathematical Society</i>. 2009;11(6):1203-1258.
    doi:<a href="https://doi.org/10.4171/jems/180">10.4171/jems/180</a>
  apa: Killip, R., Tao, T., &#38; Vişan, M. (2009). The cubic nonlinear Schrödinger
    equation in two dimensions with radial data. <i>Journal of the European Mathematical
    Society</i>. European Mathematical Society Press. <a href="https://doi.org/10.4171/jems/180">https://doi.org/10.4171/jems/180</a>
  chicago: Killip, Rowan, Terence Tao, and Monica Vişan. “The Cubic Nonlinear Schrödinger
    Equation in Two Dimensions with Radial Data.” <i>Journal of the European Mathematical
    Society</i>. European Mathematical Society Press, 2009. <a href="https://doi.org/10.4171/jems/180">https://doi.org/10.4171/jems/180</a>.
  ieee: R. Killip, T. Tao, and M. Vişan, “The cubic nonlinear Schrödinger equation
    in two dimensions with radial data,” <i>Journal of the European Mathematical Society</i>,
    vol. 11, no. 6. European Mathematical Society Press, pp. 1203–1258, 2009.
  ista: Killip R, Tao T, Vişan M. 2009. The cubic nonlinear Schrödinger equation in
    two dimensions with radial data. Journal of the European Mathematical Society.
    11(6), 1203–1258.
  mla: Killip, Rowan, et al. “The Cubic Nonlinear Schrödinger Equation in Two Dimensions
    with Radial Data.” <i>Journal of the European Mathematical Society</i>, vol. 11,
    no. 6, European Mathematical Society Press, 2009, pp. 1203–58, doi:<a href="https://doi.org/10.4171/jems/180">10.4171/jems/180</a>.
  short: R. Killip, T. Tao, M. Vişan, Journal of the European Mathematical Society
    11 (2009) 1203–1258.
das_tickbox: '1'
date_created: 2026-06-19T08:49:58Z
date_published: 2009-12-23T00:00:00Z
date_updated: 2026-07-01T12:57:57Z
day: '23'
doi: 10.4171/jems/180
extern: '1'
external_id:
  arxiv:
  - '0707.3188'
intvolume: '        11'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.0707.3188
month: '12'
oa: 1
oa_version: Preprint
page: 1203-1258
publication: Journal of the European Mathematical Society
publication_identifier:
  eissn:
  - 1435-9863
  issn:
  - 1435-9855
publication_status: published
publisher: European Mathematical Society Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: The cubic nonlinear Schrödinger equation in two dimensions with radial data
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 11
year: '2009'
...