---
OA_place: repository
OA_type: green
_id: '22082'
abstract:
- lang: eng
  text: "We establish global well-posedness and scattering for solutions to the mass-critical
    nonlinear Schrödinger equation (mathematical formular)  for large spherically
    symmetric L2/x(R^d) initial data in dimensions d >= 3.\r\nIn the focusing case
    we require that the mass is strictly less than that of the ground state. As a
    consequence, we obtain that in the focusing case, any spherically symmetric blowup
    solution must concentrate at least the mass of the ground state at the blowup
    time."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Rowan
  full_name: Killip, Rowan
  last_name: Killip
- first_name: Monica
  full_name: Visan, Monica
  id: 056daca0-b8d1-11f0-964f-f91054abf8ca
  last_name: Visan
- first_name: Xiaoyi
  full_name: Zhang, Xiaoyi
  last_name: Zhang
citation:
  ama: Killip R, Vişan M, Zhang X. The mass-critical nonlinear Schrödinger equation
    with radial data in dimensions three and higher. <i>Analysis &#38; PDE</i>. 2008;1(2):229-266.
    doi:<a href="https://doi.org/10.2140/apde.2008.1.229">10.2140/apde.2008.1.229</a>
  apa: Killip, R., Vişan, M., &#38; Zhang, X. (2008). The mass-critical nonlinear
    Schrödinger equation with radial data in dimensions three and higher. <i>Analysis
    &#38; PDE</i>. Mathematical Sciences Publishers. <a href="https://doi.org/10.2140/apde.2008.1.229">https://doi.org/10.2140/apde.2008.1.229</a>
  chicago: Killip, Rowan, Monica Vişan, and Xiaoyi Zhang. “The Mass-Critical Nonlinear
    Schrödinger Equation with Radial Data in Dimensions Three and Higher.” <i>Analysis
    &#38; PDE</i>. Mathematical Sciences Publishers, 2008. <a href="https://doi.org/10.2140/apde.2008.1.229">https://doi.org/10.2140/apde.2008.1.229</a>.
  ieee: R. Killip, M. Vişan, and X. Zhang, “The mass-critical nonlinear Schrödinger
    equation with radial data in dimensions three and higher,” <i>Analysis &#38; PDE</i>,
    vol. 1, no. 2. Mathematical Sciences Publishers, pp. 229–266, 2008.
  ista: Killip R, Vişan M, Zhang X. 2008. The mass-critical nonlinear Schrödinger
    equation with radial data in dimensions three and higher. Analysis &#38; PDE.
    1(2), 229–266.
  mla: Killip, Rowan, et al. “The Mass-Critical Nonlinear Schrödinger Equation with
    Radial Data in Dimensions Three and Higher.” <i>Analysis &#38; PDE</i>, vol. 1,
    no. 2, Mathematical Sciences Publishers, 2008, pp. 229–66, doi:<a href="https://doi.org/10.2140/apde.2008.1.229">10.2140/apde.2008.1.229</a>.
  short: R. Killip, M. Vişan, X. Zhang, Analysis &#38; PDE 1 (2008) 229–266.
das_tickbox: '1'
date_created: 2026-06-19T08:27:33Z
date_published: 2008-06-01T00:00:00Z
date_updated: 2026-07-01T07:15:15Z
day: '01'
doi: 10.2140/apde.2008.1.229
extern: '1'
external_id:
  arxiv:
  - '0708.0849'
intvolume: '         1'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.0708.0849
month: '06'
oa: 1
oa_version: Preprint
page: 229-266
publication: Analysis & PDE
publication_identifier:
  eissn:
  - 1948-206X
  issn:
  - 2157-5045
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: The mass-critical nonlinear Schrödinger equation with radial data in dimensions
  three and higher
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 1
year: '2008'
...