KdV on an incoming tide. (30th November 2021)
- Record Type:
- Journal Article
- Title:
- KdV on an incoming tide. (30th November 2021)
- Main Title:
- KdV on an incoming tide
- Authors:
- Laurens, Thierry
- Abstract:
- Abstract: Given smooth step-like initial data V (0, x ) on the real line, we show that the Korteweg–de Vries equation is globally well-posed for initial data u ( 0, x ) ∈ V ( 0, x ) + H − 1 ( R ) . The proof uses our general well-posedness result (2021 arXiv:2104.11346 ). As a prerequisite, we show that KdV is globally well-posed for H 3 ( R ) perturbations of step-like initial data. In the case V ≡ 0, we obtain a new proof of the Bona–Smith theorem (Bona and Smith 1975 Trans. R. Soc. A 278 555–601) using the low-regularity methods that established the sharp well-posedness of KdV in H −1 (Killip and Vişan 2019 Ann. Math. 190 249–305).
- Is Part Of:
- Nonlinearity. Volume 35:Number 1(2022)
- Journal:
- Nonlinearity
- Issue:
- Volume 35:Number 1(2022)
- Issue Display:
- Volume 35, Issue 1 (2022)
- Year:
- 2022
- Volume:
- 35
- Issue:
- 1
- Issue Sort Value:
- 2022-0035-0001-0000
- Page Start:
- 343
- Page End:
- 387
- Publication Date:
- 2021-11-30
- Subjects:
- KdV equation -- dispersive PDEs -- integrable systems
35Q53
Nonlinear theories -- Periodicals
Mathematical analysis -- Periodicals
Mathematical analysis
Nonlinear theories
Periodicals
515 - Journal URLs:
- http://www.iop.org/Journals/no ↗
http://iopscience.iop.org/0951-7715/ ↗
http://ioppublishing.org/ ↗ - DOI:
- 10.1088/1361-6544/ac37f5 ↗
- Languages:
- English
- ISSNs:
- 0951-7715
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library DSC - BLDSS-3PM
British Library STI - ELD Digital store - Ingest File:
- 20153.xml