Journal of Nonlinear Mathematical Physics

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Volume 11, Issue 4, November 2004, Pages 472 - 479

Uniqueness Issues on Permanent Progressive Water-Waves

Authors
K. Kobayashi, H. Okamoto
Corresponding Author
K. Kobayashi
Available Online 1 November 2004.
DOI
10.2991/jnmp.2004.11.4.4How to use a DOI?
Abstract

We consider two-dimensional water-waves of permanent shape with a constant proagation speed. Two theorems concerning the uniqueness of certain solutions are rported. Uniqueness of Crapper's pure capillary waves is proved under a positivity assumption. The proof is based on the theory of positive operators. Also proved is the uniqueness of the positive gravity waves of infinite depth with moderately large amplitude. This is accomplished by a combination of new inequalities and a numerical verification algorithm. Possibilities and impossibilities of other uniqueness theorems are discussed.

Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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<Previous Article In Issue
Next Article In Issue>
Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
11 - 4
Pages
472 - 479
Publication Date
2004/11/01
ISBN
91-974824-1-2
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.2004.11.4.4How to use a DOI?
Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - K. Kobayashi
AU  - H. Okamoto
PY  - 2004
DA  - 2004/11/01
TI  - Uniqueness Issues on Permanent Progressive Water-Waves
JO  - Journal of Nonlinear Mathematical Physics
SP  - 472
EP  - 479
VL  - 11
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2004.11.4.4
DO  - 10.2991/jnmp.2004.11.4.4
ID  - Kobayashi2004
ER  -