Nonexistence of Subcritical Solitary Waves
(2021) In Archive for Rational Mechanics and Analysis 241(1). p.535-552- Abstract
We prove the nonexistence of two-dimensional solitary gravity water waves with subcritical wave speeds and an arbitrary distribution of vorticity. This is a longstanding open problem, and even in the irrotational case there are only partial results relying on sign conditions or smallness assumptions. As a corollary, we obtain a relatively complete classification of solitary waves: they must be supercritical, symmetric, and monotonically decreasing on either side of a central crest. The proof introduces a new function which is related to the so-called flow force and has several surprising properties. In addition to solitary waves, our nonexistence result applies to “half-solitary” waves (e.g. bores) which decay in only one direction.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/7b083f52-9d94-4017-ada6-bac7e1f64173
- author
- Kozlov, Vladimir ; Lokharu, Evgeniy LU and Wheeler, Miles H.
- publishing date
- 2021-07
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Archive for Rational Mechanics and Analysis
- volume
- 241
- issue
- 1
- pages
- 18 pages
- publisher
- Springer
- external identifiers
-
- scopus:85106319759
- ISSN
- 0003-9527
- DOI
- 10.1007/s00205-021-01659-y
- language
- English
- LU publication?
- no
- additional info
- Funding Information: Large parts of this research were carried out while E.L. and M.H.W. were at Mathematisches Forschungsinstitut Oberwolfach for a Research in Pairs program. V.K. was supported by the Swedish Research Council (VR), 2017-03837. Publisher Copyright: © 2021, The Author(s).
- id
- 7b083f52-9d94-4017-ada6-bac7e1f64173
- date added to LUP
- 2023-11-03 13:19:49
- date last changed
- 2023-12-04 08:50:07
@article{7b083f52-9d94-4017-ada6-bac7e1f64173,
abstract = {{<p>We prove the nonexistence of two-dimensional solitary gravity water waves with subcritical wave speeds and an arbitrary distribution of vorticity. This is a longstanding open problem, and even in the irrotational case there are only partial results relying on sign conditions or smallness assumptions. As a corollary, we obtain a relatively complete classification of solitary waves: they must be supercritical, symmetric, and monotonically decreasing on either side of a central crest. The proof introduces a new function which is related to the so-called flow force and has several surprising properties. In addition to solitary waves, our nonexistence result applies to “half-solitary” waves (e.g. bores) which decay in only one direction.</p>}},
author = {{Kozlov, Vladimir and Lokharu, Evgeniy and Wheeler, Miles H.}},
issn = {{0003-9527}},
language = {{eng}},
number = {{1}},
pages = {{535--552}},
publisher = {{Springer}},
series = {{Archive for Rational Mechanics and Analysis}},
title = {{Nonexistence of Subcritical Solitary Waves}},
url = {{http://dx.doi.org/10.1007/s00205-021-01659-y}},
doi = {{10.1007/s00205-021-01659-y}},
volume = {{241}},
year = {{2021}},
}