---
OA_place: repository
OA_type: green
_id: '22086'
abstract:
- lang: eng
  text: We develop the existence, uniqueness, continuity, stability, and scattering
    theory for energy-critical nonlinear Schrödinger equations in dimensions n ≥ 3,
    for solutions which have large, but finite, energy and large, but finite, Strichartz
    norms. For dimensions n ≤ 6, this theory is a standard extension of the small
    data well-posedness theory based on iteration in Strichartz spaces. However, in
    dimensions n > 6 there is an obstruction to this approach because of the subquadratic
    nature of the nonlinearity (which makes the derivative of the nonlinearity non-Lipschitz).
    We resolve this by iterating in exotic Strichartz spaces instead. The theory developed
    here will be applied in a subsequent paper of the second author, [21], to establish
    global well-posedness and scattering for the defocusing energy-critical equation
    for large energy data.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- 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: Tao T, Vişan M. Stability of energy-critical nonlinear Schrodinger equations
    in high dimensions. <i>Electronic Journal of Differential Equations</i>. 2005;2005(118):1-28.
  apa: Tao, T., &#38; Vişan, M. (2005). Stability of energy-critical nonlinear Schrodinger
    equations in high dimensions. <i>Electronic Journal of Differential Equations</i>.
    Texas State University.
  chicago: Tao, Terence, and Monica Vişan. “Stability of Energy-Critical Nonlinear
    Schrodinger Equations in High Dimensions.” <i>Electronic Journal of Differential
    Equations</i>. Texas State University, 2005.
  ieee: T. Tao and M. Vişan, “Stability of energy-critical nonlinear Schrodinger equations
    in high dimensions,” <i>Electronic Journal of Differential Equations</i>, vol.
    2005, no. 118. Texas State University, pp. 1–28, 2005.
  ista: Tao T, Vişan M. 2005. Stability of energy-critical nonlinear Schrodinger equations
    in high dimensions. Electronic Journal of Differential Equations. 2005(118), 1–28.
  mla: Tao, Terence, and Monica Vişan. “Stability of Energy-Critical Nonlinear Schrodinger
    Equations in High Dimensions.” <i>Electronic Journal of Differential Equations</i>,
    vol. 2005, no. 118, Texas State University, 2005, pp. 1–28.
  short: T. Tao, M. Vişan, Electronic Journal of Differential Equations 2005 (2005)
    1–28.
das_tickbox: '1'
date_created: 2026-06-19T08:44:06Z
date_published: 2005-10-26T00:00:00Z
date_updated: 2026-07-01T12:31:43Z
day: '26'
extern: '1'
external_id:
  arxiv:
  - math/0507005
intvolume: '      2005'
issue: '118'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.math/0507005
mathsc:
- 35J10
month: '10'
oa: 1
oa_version: Preprint
page: 1-28
publication: Electronic Journal of Differential Equations
publication_identifier:
  eissn:
  - 1550-6150
publication_status: published
publisher: Texas State University
quality_controlled: '1'
scopus_import: '1'
status: public
title: Stability of energy-critical nonlinear Schrodinger equations in high dimensions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2005
year: '2005'
...