---
OA_place: repository
OA_type: green
_id: '22054'
abstract:
- lang: eng
  text: We consider the Korteweg–de Vries equation with white noise initial data,
    posed on the whole real line, and prove the almost sure existence of solutions.
    Moreover, we show that the solutions obey the group property and follow a white
    noise law at all times, past or future. As an offshoot of our methods, we also
    obtain a new proof of the existence of solutions and the invariance of white noise
    measure in the torus setting.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Rowan
  full_name: Killip, Rowan
  last_name: Killip
- first_name: Jason
  full_name: Murphy, Jason
  last_name: Murphy
- first_name: Monica
  full_name: Visan, Monica
  id: 056daca0-b8d1-11f0-964f-f91054abf8ca
  last_name: Visan
citation:
  ama: Killip R, Murphy J, Vişan M. Invariance of white noise for KdV on the line.
    <i>Inventiones mathematicae</i>. 2020;222(1):203-282. doi:<a href="https://doi.org/10.1007/s00222-020-00964-9">10.1007/s00222-020-00964-9</a>
  apa: Killip, R., Murphy, J., &#38; Vişan, M. (2020). Invariance of white noise for
    KdV on the line. <i>Inventiones Mathematicae</i>. Springer Nature. <a href="https://doi.org/10.1007/s00222-020-00964-9">https://doi.org/10.1007/s00222-020-00964-9</a>
  chicago: Killip, Rowan, Jason Murphy, and Monica Vişan. “Invariance of White Noise
    for KdV on the Line.” <i>Inventiones Mathematicae</i>. Springer Nature, 2020.
    <a href="https://doi.org/10.1007/s00222-020-00964-9">https://doi.org/10.1007/s00222-020-00964-9</a>.
  ieee: R. Killip, J. Murphy, and M. Vişan, “Invariance of white noise for KdV on
    the line,” <i>Inventiones mathematicae</i>, vol. 222, no. 1. Springer Nature,
    pp. 203–282, 2020.
  ista: Killip R, Murphy J, Vişan M. 2020. Invariance of white noise for KdV on the
    line. Inventiones mathematicae. 222(1), 203–282.
  mla: Killip, Rowan, et al. “Invariance of White Noise for KdV on the Line.” <i>Inventiones
    Mathematicae</i>, vol. 222, no. 1, Springer Nature, 2020, pp. 203–82, doi:<a href="https://doi.org/10.1007/s00222-020-00964-9">10.1007/s00222-020-00964-9</a>.
  short: R. Killip, J. Murphy, M. Vişan, Inventiones Mathematicae 222 (2020) 203–282.
das_tickbox: '1'
date_created: 2026-06-19T07:56:16Z
date_published: 2020-10-01T00:00:00Z
date_updated: 2026-06-25T08:39:30Z
day: '01'
doi: 10.1007/s00222-020-00964-9
extern: '1'
external_id:
  arxiv:
  - '1904.11910'
intvolume: '       222'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1904.11910
month: '10'
oa: 1
oa_version: Preprint
page: 203-282
publication: Inventiones mathematicae
publication_identifier:
  eissn:
  - 1432-1297
  issn:
  - 0020-9910
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Invariance of white noise for KdV on the line
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 222
year: '2020'
...