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Global conservative solutions of the Camassa-Holm equation

Bressan, Alberto and Constantin, Adrian LU (2007) In Archive for Rational Mechanics and Analysis 183(2). p.215-239
Abstract
This paper develops a new approach in the analysis of the Camassa-Holm equation. By introducing a new set of independent and dependent variables, the equation is transformed into a semilinear system, whose solutions are obtained as fixed points of a contractive transformation. These new variables resolve all singularities due to possible wave breaking. Returning to the original variables, we obtain a semigroup of global solutions, depending continuously on the initial data. Our solutions are conservative, in the sense that the total energy equals a constant, for almost every time.
Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Archive for Rational Mechanics and Analysis
volume
183
issue
2
pages
215 - 239
publisher
Springer
external identifiers
  • wos:000244023300002
  • scopus:33846878957
ISSN
0003-9527
DOI
10.1007/s00205-006-0010-z
language
English
LU publication?
yes
id
51de39cb-2451-4950-9591-4cd6c9618431 (old id 675324)
date added to LUP
2016-04-01 12:30:54
date last changed
2022-04-21 08:21:38
@article{51de39cb-2451-4950-9591-4cd6c9618431,
  abstract     = {{This paper develops a new approach in the analysis of the Camassa-Holm equation. By introducing a new set of independent and dependent variables, the equation is transformed into a semilinear system, whose solutions are obtained as fixed points of a contractive transformation. These new variables resolve all singularities due to possible wave breaking. Returning to the original variables, we obtain a semigroup of global solutions, depending continuously on the initial data. Our solutions are conservative, in the sense that the total energy equals a constant, for almost every time.}},
  author       = {{Bressan, Alberto and Constantin, Adrian}},
  issn         = {{0003-9527}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{215--239}},
  publisher    = {{Springer}},
  series       = {{Archive for Rational Mechanics and Analysis}},
  title        = {{Global conservative solutions of the Camassa-Holm equation}},
  url          = {{http://dx.doi.org/10.1007/s00205-006-0010-z}},
  doi          = {{10.1007/s00205-006-0010-z}},
  volume       = {{183}},
  year         = {{2007}},
}