---
OA_place: repository
OA_type: green
_id: '22052'
abstract:
- lang: eng
  text: 'We consider the focusing cubic nonlinear Schrödinger equation (NLS) in the
    exterior Ω of a smooth, compact, strictly convex obstacle in three dimensions.
    We prove that the threshold for global existence and scattering is the same as
    for the problem posed on Euclidean space. Specifically, we prove that if E(u0)M(u0)<E(Q)M(Q)
    and ||u0||2||u0||2<\|\nabla Q||2||Q||2, the corresponding solution to the initial
    value problem with Dirichlet boundary conditions exists globally and scatters
    to linear evolutions asymptotically in the future and in the past. Here, Q(x)
    denotes the ground state for the focusing cubic NLS in ℝ3. '
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 focusing cubic NLS on exterior domains in three
    dimensions. <i>Applied Mathematics Research eXpress</i>. 2016;2016(1):146-180.
    doi:<a href="https://doi.org/10.1093/amrx/abv012">10.1093/amrx/abv012</a>
  apa: Killip, R., Vişan, M., &#38; Zhang, X. (2016). The focusing cubic NLS on exterior
    domains in three dimensions. <i>Applied Mathematics Research EXpress</i>. Oxford
    University Press. <a href="https://doi.org/10.1093/amrx/abv012">https://doi.org/10.1093/amrx/abv012</a>
  chicago: Killip, Rowan, Monica Vişan, and Xiaoyi Zhang. “The Focusing Cubic NLS
    on Exterior Domains in Three Dimensions.” <i>Applied Mathematics Research EXpress</i>.
    Oxford University Press, 2016. <a href="https://doi.org/10.1093/amrx/abv012">https://doi.org/10.1093/amrx/abv012</a>.
  ieee: R. Killip, M. Vişan, and X. Zhang, “The focusing cubic NLS on exterior domains
    in three dimensions,” <i>Applied Mathematics Research eXpress</i>, vol. 2016,
    no. 1. Oxford University Press, pp. 146–180, 2016.
  ista: Killip R, Vişan M, Zhang X. 2016. The focusing cubic NLS on exterior domains
    in three dimensions. Applied Mathematics Research eXpress. 2016(1), 146–180.
  mla: Killip, Rowan, et al. “The Focusing Cubic NLS on Exterior Domains in Three
    Dimensions.” <i>Applied Mathematics Research EXpress</i>, vol. 2016, no. 1, Oxford
    University Press, 2016, pp. 146–80, doi:<a href="https://doi.org/10.1093/amrx/abv012">10.1093/amrx/abv012</a>.
  short: R. Killip, M. Vişan, X. Zhang, Applied Mathematics Research EXpress 2016
    (2016) 146–180.
das_tickbox: '1'
date_created: 2026-06-19T07:54:24Z
date_published: 2016-01-01T00:00:00Z
date_updated: 2026-06-25T08:30:19Z
day: '01'
doi: 10.1093/amrx/abv012
extern: '1'
external_id:
  arxiv:
  - '1501.05062'
intvolume: '      2016'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1501.05062
month: '01'
oa: 1
oa_version: Preprint
page: 146-180
publication: Applied Mathematics Research eXpress
publication_identifier:
  eissn:
  - 1687-1197
  issn:
  - 1687-1200
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: The focusing cubic NLS on exterior domains in three dimensions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2016
year: '2016'
...