---
OA_place: repository
OA_type: green
_id: '22021'
abstract:
- lang: eng
  text: "We establish global well-posedness for both the defocusing and\r\nfocusing
    complex-valued modified Korteweg–de Vries equations on the real line\r\nin modulation
    spaces Ms,2p (R), for all 1 \x14 p < 1 and 0 \x14 s < 3/2 − 1/p. We\r\nwill also
    show that such solutions admit global-in-time bounds in these spaces\r\nand that
    equicontinuous sets of initial data lead to equicontinuous ensembles\r\nof orbits.
    Indeed, such information forms a crucial part of our well-posedness\r\nargument."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Saikatul
  full_name: Haque, Saikatul
  last_name: Haque
- 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: Yunfeng
  full_name: Zhang, Yunfeng
  last_name: Zhang
citation:
  ama: Haque S, Killip R, Vişan M, Zhang Y.  Global well-posedness and equicontinuity
    for modified Korteweg–de Vries equations in modulation spaces. <i>Pure and Applied
    Analysis</i>. 2025;7(3):615-637. doi:<a href="https://doi.org/10.2140/paa.2025.7.615">10.2140/paa.2025.7.615</a>
  apa: Haque, S., Killip, R., Vişan, M., &#38; Zhang, Y. (2025).  Global well-posedness
    and equicontinuity for modified Korteweg–de Vries equations in modulation spaces.
    <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers. <a href="https://doi.org/10.2140/paa.2025.7.615">https://doi.org/10.2140/paa.2025.7.615</a>
  chicago: Haque, Saikatul, Rowan Killip, Monica Vişan, and Yunfeng Zhang. “ Global
    Well-Posedness and Equicontinuity for Modified Korteweg–de Vries Equations in
    Modulation Spaces.” <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers,
    2025. <a href="https://doi.org/10.2140/paa.2025.7.615">https://doi.org/10.2140/paa.2025.7.615</a>.
  ieee: S. Haque, R. Killip, M. Vişan, and Y. Zhang, “ Global well-posedness and equicontinuity
    for modified Korteweg–de Vries equations in modulation spaces,” <i>Pure and Applied
    Analysis</i>, vol. 7, no. 3. Mathematical Sciences Publishers, pp. 615–637, 2025.
  ista: Haque S, Killip R, Vişan M, Zhang Y. 2025.  Global well-posedness and equicontinuity
    for modified Korteweg–de Vries equations in modulation spaces. Pure and Applied
    Analysis. 7(3), 615–637.
  mla: Haque, Saikatul, et al. “ Global Well-Posedness and Equicontinuity for Modified
    Korteweg–de Vries Equations in Modulation Spaces.” <i>Pure and Applied Analysis</i>,
    vol. 7, no. 3, Mathematical Sciences Publishers, 2025, pp. 615–37, doi:<a href="https://doi.org/10.2140/paa.2025.7.615">10.2140/paa.2025.7.615</a>.
  short: S. Haque, R. Killip, M. Vişan, Y. Zhang, Pure and Applied Analysis 7 (2025)
    615–637.
date_created: 2026-06-19T07:30:23Z
date_published: 2025-06-18T00:00:00Z
date_updated: 2026-06-19T10:16:14Z
day: '18'
doi: 10.2140/paa.2025.7.615
extern: '1'
external_id:
  arxiv:
  - '2411.05300'
intvolume: '         7'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2411.05300
month: '06'
oa: 1
oa_version: Preprint
page: 615-637
publication: Pure and Applied Analysis
publication_identifier:
  eissn:
  - 2578-5885
  issn:
  - 2578-5893
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: ' Global well-posedness and equicontinuity for modified Korteweg–de Vries equations
  in modulation spaces'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 7
year: '2025'
...