---
OA_place: repository
OA_type: green
_id: '22081'
abstract:
- lang: eng
  text: We consider the Cauchy problem for a family of semilinear defocusing Schrödinger
    equations with monomial nonlinearities in one space dimension. We establish global
    well-posedness and scattering. Our analysis is based on a four-particle interaction
    Morawetz estimate giving a priori $L_{t,x}^8$ spacetime control on solutions.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: J.
  full_name: Colliander, J.
  last_name: Colliander
- first_name: Justin
  full_name: Holmer, Justin
  last_name: Holmer
- 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: Colliander J, Holmer J, Vişan M, Zhang X. Global existence and scattering for
    rough solutions to generalized nonlinear Schrödinger equations on $R$. <i>Communications
    on Pure and Applied Analysis</i>. 2008;7(3):467-489. doi:<a href="https://doi.org/10.3934/cpaa.2008.7.467">10.3934/cpaa.2008.7.467</a>
  apa: Colliander, J., Holmer, J., Vişan, M., &#38; Zhang, X. (2008). Global existence
    and scattering for rough solutions to generalized nonlinear Schrödinger equations
    on $R$. <i>Communications on Pure and Applied Analysis</i>. American Institute
    of Mathematical Sciences. <a href="https://doi.org/10.3934/cpaa.2008.7.467">https://doi.org/10.3934/cpaa.2008.7.467</a>
  chicago: Colliander, J., Justin Holmer, Monica Vişan, and Xiaoyi Zhang. “Global
    Existence and Scattering for Rough Solutions to Generalized Nonlinear Schrödinger
    Equations on $R$.” <i>Communications on Pure and Applied Analysis</i>. American
    Institute of Mathematical Sciences, 2008. <a href="https://doi.org/10.3934/cpaa.2008.7.467">https://doi.org/10.3934/cpaa.2008.7.467</a>.
  ieee: J. Colliander, J. Holmer, M. Vişan, and X. Zhang, “Global existence and scattering
    for rough solutions to generalized nonlinear Schrödinger equations on $R$,” <i>Communications
    on Pure and Applied Analysis</i>, vol. 7, no. 3. American Institute of Mathematical
    Sciences, pp. 467–489, 2008.
  ista: Colliander J, Holmer J, Vişan M, Zhang X. 2008. Global existence and scattering
    for rough solutions to generalized nonlinear Schrödinger equations on $R$. Communications
    on Pure and Applied Analysis. 7(3), 467–489.
  mla: Colliander, J., et al. “Global Existence and Scattering for Rough Solutions
    to Generalized Nonlinear Schrödinger Equations on $R$.” <i>Communications on Pure
    and Applied Analysis</i>, vol. 7, no. 3, American Institute of Mathematical Sciences,
    2008, pp. 467–89, doi:<a href="https://doi.org/10.3934/cpaa.2008.7.467">10.3934/cpaa.2008.7.467</a>.
  short: J. Colliander, J. Holmer, M. Vişan, X. Zhang, Communications on Pure and
    Applied Analysis 7 (2008) 467–489.
das_tickbox: '1'
date_created: 2026-06-19T08:27:11Z
date_published: 2008-03-01T00:00:00Z
date_updated: 2026-07-01T07:05:55Z
day: '01'
doi: 10.3934/cpaa.2008.7.467
extern: '1'
external_id:
  arxiv:
  - math/0612452
intvolume: '         7'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.math/0612452
mathsc:
- 35Q55
month: '03'
oa: 1
oa_version: Preprint
page: 467-489
publication: Communications on Pure and Applied Analysis
publication_identifier:
  eissn:
  - 1553-5258
  issn:
  - 1534-0392
publication_status: published
publisher: American Institute of Mathematical Sciences
quality_controlled: '1'
scopus_import: '1'
status: public
title: Global existence and scattering for rough solutions to generalized nonlinear
  Schrödinger equations on $R$
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 7
year: '2008'
...