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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
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
2007-12-11 15:55:35
date last changed
2017-11-12 03:31:23
@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},
  volume       = {183},
  year         = {2007},
}