---
OA_place: repository
OA_type: green
_id: '22072'
abstract:
- lang: eng
  text: We consider the derivative nonlinear Schrödinger equation in one spatial dimension,
    which is known to be completely integrable. We prove that the orbits of L^2 bounded
    and equicontinuous sets of initial data remain bounded and equicontinuous, not
    only under this flow, but also under the entire hierarchy. This allows us to remove
    the small-data restriction from prior conservation laws and global well-posedness
    results.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Benjamin
  full_name: Harrop-Griffiths, Benjamin
  last_name: Harrop-Griffiths
- 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: Harrop-Griffiths B, Killip R, Vişan M. Large-data equicontinuity for the derivative
    NLS. <i>International Mathematics Research Notices</i>. 2023;2023(6):4601-4642.
    doi:<a href="https://doi.org/10.1093/imrn/rnab374">10.1093/imrn/rnab374</a>
  apa: Harrop-Griffiths, B., Killip, R., &#38; Vişan, M. (2023). Large-data equicontinuity
    for the derivative NLS. <i>International Mathematics Research Notices</i>. Oxford
    University Press. <a href="https://doi.org/10.1093/imrn/rnab374">https://doi.org/10.1093/imrn/rnab374</a>
  chicago: Harrop-Griffiths, Benjamin, Rowan Killip, and Monica Vişan. “Large-Data
    Equicontinuity for the Derivative NLS.” <i>International Mathematics Research
    Notices</i>. Oxford University Press, 2023. <a href="https://doi.org/10.1093/imrn/rnab374">https://doi.org/10.1093/imrn/rnab374</a>.
  ieee: B. Harrop-Griffiths, R. Killip, and M. Vişan, “Large-data equicontinuity for
    the derivative NLS,” <i>International Mathematics Research Notices</i>, vol. 2023,
    no. 6. Oxford University Press, pp. 4601–4642, 2023.
  ista: Harrop-Griffiths B, Killip R, Vişan M. 2023. Large-data equicontinuity for
    the derivative NLS. International Mathematics Research Notices. 2023(6), 4601–4642.
  mla: Harrop-Griffiths, Benjamin, et al. “Large-Data Equicontinuity for the Derivative
    NLS.” <i>International Mathematics Research Notices</i>, vol. 2023, no. 6, Oxford
    University Press, 2023, pp. 4601–42, doi:<a href="https://doi.org/10.1093/imrn/rnab374">10.1093/imrn/rnab374</a>.
  short: B. Harrop-Griffiths, R. Killip, M. Vişan, International Mathematics Research
    Notices 2023 (2023) 4601–4642.
das_tickbox: '1'
date_created: 2026-06-19T08:22:03Z
date_published: 2023-03-01T00:00:00Z
date_updated: 2026-06-30T10:56:42Z
day: '01'
doi: 10.1093/imrn/rnab374
extern: '1'
external_id:
  arxiv:
  - '2106.13333'
intvolume: '      2023'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2106.13333
month: '03'
oa: 1
oa_version: Preprint
page: 4601-4642
publication: International Mathematics Research Notices
publication_identifier:
  eissn:
  - 1687-0247
  issn:
  - 1073-7928
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Large-data equicontinuity for the derivative NLS
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2023
year: '2023'
...