Global Conservative Solutions of the Camassa–Holm Equation

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 re...

Full description

Saved in:
Bibliographic Details
Published in:Archive for rational mechanics and analysis Vol. 183; no. 2; pp. 215 - 239
Main Authors: Bressan, Alberto, Constantin, Adrian
Format: Journal Article
Language:English
Published: Heidelberg Springer 01.02.2007
Berlin Springer Nature B.V
New York, NY
Subjects:
Applied sciences
Buildings. Public works
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
General theory
Hydraulic constructions
Matematik
Mathematical methods in physics
Mathematical Sciences
Natural Sciences
Naturvetenskap
Numerical approximation and analysis
Ordinary and partial differential equations, boundary value problems
Physics
Singularity
Semigroup
Punctual transformation
Modeling
Global solution
Wave breaking
ISSN:0003-9527, 1432-0673, 1432-0673
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.[PUBLICATION ABSTRACT]
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0003-9527
1432-0673
1432-0673
DOI:10.1007/s00205-006-0010-z