---
OA_place: repository
OA_type: green
_id: '22053'
abstract:
- lang: eng
  text: We consider the Gross–Pitaevskii equation on R^4 and the cubic-quintic nonlinear
    Schrödinger equation (NLS) on R^3 with non-vanishing boundary conditions at spatial
    infinity. By viewing these equations as perturbations to the energy-critical NLS,
    we prove that they are globally well-posed in their energy spaces. In particular,
    we prove unconditional uniqueness in the energy spaces for these equations.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Rowan
  full_name: Killip, Rowan
  last_name: Killip
- first_name: Tadahiro
  full_name: Oh, Tadahiro
  last_name: Oh
- first_name: Oana
  full_name: Pocovnicu, Oana
  last_name: Pocovnicu
- first_name: Monica
  full_name: Visan, Monica
  id: 056daca0-b8d1-11f0-964f-f91054abf8ca
  last_name: Visan
citation:
  ama: Killip R, Oh T, Pocovnicu O, Vişan M. Global well-posedness of the Gross–Pitaevskii
    and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary
    conditions. <i>Mathematical Research Letters</i>. 2013;19(5):969-986. doi:<a href="https://doi.org/10.4310/mrl.2012.v19.n5.a1">10.4310/mrl.2012.v19.n5.a1</a>
  apa: Killip, R., Oh, T., Pocovnicu, O., &#38; Vişan, M. (2013). Global well-posedness
    of the Gross–Pitaevskii and cubic-quintic nonlinear Schrödinger equations with
    non-vanishing boundary conditions. <i>Mathematical Research Letters</i>. International
    Press of Boston. <a href="https://doi.org/10.4310/mrl.2012.v19.n5.a1">https://doi.org/10.4310/mrl.2012.v19.n5.a1</a>
  chicago: Killip, Rowan, Tadahiro Oh, Oana Pocovnicu, and Monica Vişan. “Global Well-Posedness
    of the Gross–Pitaevskii and Cubic-Quintic Nonlinear Schrödinger Equations with
    Non-Vanishing Boundary Conditions.” <i>Mathematical Research Letters</i>. International
    Press of Boston, 2013. <a href="https://doi.org/10.4310/mrl.2012.v19.n5.a1">https://doi.org/10.4310/mrl.2012.v19.n5.a1</a>.
  ieee: R. Killip, T. Oh, O. Pocovnicu, and M. Vişan, “Global well-posedness of the
    Gross–Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing
    boundary conditions,” <i>Mathematical Research Letters</i>, vol. 19, no. 5. International
    Press of Boston, pp. 969–986, 2013.
  ista: Killip R, Oh T, Pocovnicu O, Vişan M. 2013. Global well-posedness of the Gross–Pitaevskii
    and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary
    conditions. Mathematical Research Letters. 19(5), 969–986.
  mla: Killip, Rowan, et al. “Global Well-Posedness of the Gross–Pitaevskii and Cubic-Quintic
    Nonlinear Schrödinger Equations with Non-Vanishing Boundary Conditions.” <i>Mathematical
    Research Letters</i>, vol. 19, no. 5, International Press of Boston, 2013, pp.
    969–86, doi:<a href="https://doi.org/10.4310/mrl.2012.v19.n5.a1">10.4310/mrl.2012.v19.n5.a1</a>.
  short: R. Killip, T. Oh, O. Pocovnicu, M. Vişan, Mathematical Research Letters 19
    (2013) 969–986.
das_tickbox: '1'
date_created: 2026-06-19T07:54:49Z
date_published: 2013-03-15T00:00:00Z
date_updated: 2026-06-25T08:33:18Z
day: '15'
doi: 10.4310/mrl.2012.v19.n5.a1
extern: '1'
external_id:
  arxiv:
  - '1112.1354'
intvolume: '        19'
issue: '5'
keyword:
- NLS
- Gross–Pitaevskii equation
- non-vanishing boundary condition
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1112.1354
mathsc:
- 35Q55
month: '03'
oa: 1
oa_version: Preprint
page: 969-986
publication: Mathematical Research Letters
publication_identifier:
  eissn:
  - 1945-001X
  issn:
  - 1073-2780
publication_status: published
publisher: International Press of Boston
quality_controlled: '1'
scopus_import: '1'
status: public
title: Global well-posedness of the Gross–Pitaevskii and cubic-quintic nonlinear Schrödinger
  equations with non-vanishing boundary conditions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 19
year: '2013'
...