---
OA_place: repository
OA_type: green
_id: '22033'
abstract:
- lang: eng
  text: "We consider the defocusing energy-critical nonlinear Schrödinger\r\nequation
    with inverse-square potential iut = −∆u + a|x|^−2u + |u|^4u in three\r\nspace
    dimensions. We prove global well-posedness and scattering for a >− 1/4 + 1/25.
    We also carry out the variational analysis needed to treat the focusing case."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Rowan
  full_name: Killip, Rowan
  last_name: Killip
- first_name: Changxing
  full_name: Miao, Changxing
  last_name: Miao
- first_name: Monica
  full_name: Visan, Monica
  id: 056daca0-b8d1-11f0-964f-f91054abf8ca
  last_name: Visan
- first_name: Junyong
  full_name: Zhang, Junyong
  last_name: Zhang
- first_name: Jiqiang
  full_name: Zheng, Jiqiang
  last_name: Zheng
citation:
  ama: Killip R, Miao C, Vişan M, Zhang J, Zheng J. The energy-critical NLS with inverse-square
    potential. <i>Discrete and Continuous Dynamical Systems</i>. 2017;37(7):3831-3866.
    doi:<a href="https://doi.org/10.3934/dcds.2017162">10.3934/dcds.2017162</a>
  apa: Killip, R., Miao, C., Vişan, M., Zhang, J., &#38; Zheng, J. (2017). The energy-critical
    NLS with inverse-square potential. <i>Discrete and Continuous Dynamical Systems</i>.
    American Institute of Mathematical Sciences. <a href="https://doi.org/10.3934/dcds.2017162">https://doi.org/10.3934/dcds.2017162</a>
  chicago: Killip, Rowan, Changxing Miao, Monica Vişan, Junyong Zhang, and Jiqiang
    Zheng. “The Energy-Critical NLS with Inverse-Square Potential.” <i>Discrete and
    Continuous Dynamical Systems</i>. American Institute of Mathematical Sciences,
    2017. <a href="https://doi.org/10.3934/dcds.2017162">https://doi.org/10.3934/dcds.2017162</a>.
  ieee: R. Killip, C. Miao, M. Vişan, J. Zhang, and J. Zheng, “The energy-critical
    NLS with inverse-square potential,” <i>Discrete and Continuous Dynamical Systems</i>,
    vol. 37, no. 7. American Institute of Mathematical Sciences, pp. 3831–3866, 2017.
  ista: Killip R, Miao C, Vişan M, Zhang J, Zheng J. 2017. The energy-critical NLS
    with inverse-square potential. Discrete and Continuous Dynamical Systems. 37(7),
    3831–3866.
  mla: Killip, Rowan, et al. “The Energy-Critical NLS with Inverse-Square Potential.”
    <i>Discrete and Continuous Dynamical Systems</i>, vol. 37, no. 7, American Institute
    of Mathematical Sciences, 2017, pp. 3831–66, doi:<a href="https://doi.org/10.3934/dcds.2017162">10.3934/dcds.2017162</a>.
  short: R. Killip, C. Miao, M. Vişan, J. Zhang, J. Zheng, Discrete and Continuous
    Dynamical Systems 37 (2017) 3831–3866.
das_tickbox: '1'
date_created: 2026-06-19T07:42:59Z
date_published: 2017-07-01T00:00:00Z
date_updated: 2026-06-22T12:47:32Z
day: '01'
doi: 10.3934/dcds.2017162
extern: '1'
external_id:
  arxiv:
  - '1509.05822'
intvolume: '        37'
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1509.05822
month: '07'
oa: 1
oa_version: Preprint
page: 3831-3866
publication: Discrete and Continuous Dynamical Systems
publication_identifier:
  eissn:
  - 1553-5231
  issn:
  - 1078-0947
publication_status: published
publisher: American Institute of Mathematical Sciences
quality_controlled: '1'
scopus_import: '1'
status: public
title: The energy-critical NLS with inverse-square potential
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 37
year: '2017'
...