---
OA_place: publisher
OA_type: diamond
_id: '22067'
abstract:
- lang: eng
  text: "We consider the derivative nonlinear Schrödinger equation in one space dimension,
    posed both on the line and on the circle. This model is known to be completely
    integrable and L^2-critical with respect to scaling. We first discuss whether
    ensembles of orbits with L^2-equicontinuous initial data remain equicontinuous
    under evolution. We prove that this is true under the restriction \r\nM(q)=∫∣∣q∣∣2<4π.
    We conjecture that this restriction is unnecessary. Further, we prove that the
    problem is globally well posed for initial data in H1∕6 under the same restriction
    on M. Moreover, we show that this restriction would be removed by a successful
    resolution of our equicontinuity conjecture."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Rowan
  full_name: Killip, Rowan
  last_name: Killip
- first_name: Maria
  full_name: Ntekoume, Maria
  last_name: Ntekoume
- first_name: Monica
  full_name: Visan, Monica
  id: 056daca0-b8d1-11f0-964f-f91054abf8ca
  last_name: Visan
citation:
  ama: Killip R, Ntekoume M, Vişan M. On the well-posedness problem for the derivativenonlinear
    Schrödinger equation. <i>Analysis &#38; PDE</i>. 2023;16(5):1245-1270. doi:<a
    href="https://doi.org/10.2140/apde.2023.16.1245">10.2140/apde.2023.16.1245</a>
  apa: Killip, R., Ntekoume, M., &#38; Vişan, M. (2023). On the well-posedness problem
    for the derivativenonlinear Schrödinger equation. <i>Analysis &#38; PDE</i>. Mathematical
    Sciences Publishers. <a href="https://doi.org/10.2140/apde.2023.16.1245">https://doi.org/10.2140/apde.2023.16.1245</a>
  chicago: Killip, Rowan, Maria Ntekoume, and Monica Vişan. “On the Well-Posedness
    Problem for the Derivativenonlinear Schrödinger Equation.” <i>Analysis &#38; PDE</i>.
    Mathematical Sciences Publishers, 2023. <a href="https://doi.org/10.2140/apde.2023.16.1245">https://doi.org/10.2140/apde.2023.16.1245</a>.
  ieee: R. Killip, M. Ntekoume, and M. Vişan, “On the well-posedness problem for the
    derivativenonlinear Schrödinger equation,” <i>Analysis &#38; PDE</i>, vol. 16,
    no. 5. Mathematical Sciences Publishers, pp. 1245–1270, 2023.
  ista: Killip R, Ntekoume M, Vişan M. 2023. On the well-posedness problem for the
    derivativenonlinear Schrödinger equation. Analysis &#38; PDE. 16(5), 1245–1270.
  mla: Killip, Rowan, et al. “On the Well-Posedness Problem for the Derivativenonlinear
    Schrödinger Equation.” <i>Analysis &#38; PDE</i>, vol. 16, no. 5, Mathematical
    Sciences Publishers, 2023, pp. 1245–70, doi:<a href="https://doi.org/10.2140/apde.2023.16.1245">10.2140/apde.2023.16.1245</a>.
  short: R. Killip, M. Ntekoume, M. Vişan, Analysis &#38; PDE 16 (2023) 1245–1270.
das_tickbox: '1'
date_created: 2026-06-19T08:15:32Z
date_published: 2023-08-12T00:00:00Z
date_updated: 2026-06-30T07:20:56Z
day: '12'
ddc:
- '500'
doi: 10.2140/apde.2023.16.1245
extern: '1'
external_id:
  arxiv:
  - '2101.12274'
has_accepted_license: '1'
intvolume: '        16'
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.2140/apde.2023.16.1245
mathsc:
- 35Q55
month: '08'
oa: 1
oa_version: Published Version
page: 1245-1270
publication: Analysis & PDE
publication_identifier:
  eissn:
  - 1948-206X
  issn:
  - 2157-5045
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the well-posedness problem for the derivativenonlinear Schrödinger equation
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 16
year: '2023'
...