---
OA_place: repository
OA_type: green
_id: '22038'
abstract:
- lang: eng
  text: We prove global well-posedness of the fifth-order Korteweg-de Vries equation
    on the real line for initial data in H^-1(R). Global well-posedness in L^2(R)
    was shown previously in [8] using the method of commuting flows. Since this method
    is insensitive to the ambient geometry, it cannot go beyond the sharp L^2 threshold
    for the torus demonstrated in [3]. To prove our result, we introduce a new strategy
    that integrates dispersive effects into the method of commuting flows.
article_number: '21'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Bjoern
  full_name: Bringmann, Bjoern
  last_name: Bringmann
- 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
citation:
  ama: Bringmann B, Killip R, Vişan M. Global well-posedness for the fifth-order KdV
    equation in H^-1(R). <i>Annals of PDE</i>. 2021;7(2). doi:<a href="https://doi.org/10.1007/s40818-021-00111-4">10.1007/s40818-021-00111-4</a>
  apa: Bringmann, B., Killip, R., &#38; Vişan, M. (2021). Global well-posedness for
    the fifth-order KdV equation in H^-1(R). <i>Annals of PDE</i>. Springer Nature.
    <a href="https://doi.org/10.1007/s40818-021-00111-4">https://doi.org/10.1007/s40818-021-00111-4</a>
  chicago: Bringmann, Bjoern, Rowan Killip, and Monica Vişan. “Global Well-Posedness
    for the Fifth-Order KdV Equation in H^-1(R).” <i>Annals of PDE</i>. Springer Nature,
    2021. <a href="https://doi.org/10.1007/s40818-021-00111-4">https://doi.org/10.1007/s40818-021-00111-4</a>.
  ieee: B. Bringmann, R. Killip, and M. Vişan, “Global well-posedness for the fifth-order
    KdV equation in H^-1(R),” <i>Annals of PDE</i>, vol. 7, no. 2. Springer Nature,
    2021.
  ista: Bringmann B, Killip R, Vişan M. 2021. Global well-posedness for the fifth-order
    KdV equation in H^-1(R). Annals of PDE. 7(2), 21.
  mla: Bringmann, Bjoern, et al. “Global Well-Posedness for the Fifth-Order KdV Equation
    in H^-1(R).” <i>Annals of PDE</i>, vol. 7, no. 2, 21, Springer Nature, 2021, doi:<a
    href="https://doi.org/10.1007/s40818-021-00111-4">10.1007/s40818-021-00111-4</a>.
  short: B. Bringmann, R. Killip, M. Vişan, Annals of PDE 7 (2021).
das_tickbox: '1'
date_created: 2026-06-19T07:44:49Z
date_published: 2021-08-25T00:00:00Z
date_updated: 2026-06-22T13:03:48Z
day: '25'
doi: 10.1007/s40818-021-00111-4
extern: '1'
external_id:
  arxiv:
  - '1912.01536'
intvolume: '         7'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1912.01536
month: '08'
oa: 1
oa_version: Preprint
publication: Annals of PDE
publication_identifier:
  eissn:
  - 2199-2576
  issn:
  - 2524-5317
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Global well-posedness for the fifth-order KdV equation in H^-1(R)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 7
year: '2021'
...