Global conservative solutions of the Camassa-Holm equation

Alberto Bressan, Adrian Constantin

Research output: Contribution to journalReview article

490 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)215-239
Number of pages25
JournalArchive for Rational Mechanics and Analysis
Volume183
Issue number2
DOIs
StatePublished - Feb 1 2007

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Camassa-Holm Equation
Wave Breaking
Semilinear Systems
Global Solution
Resolve
Semigroup
Fixed point
Singularity
Dependent
Energy

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Cite this

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Global conservative solutions of the Camassa-Holm equation. / Bressan, Alberto; Constantin, Adrian.

In: Archive for Rational Mechanics and Analysis, Vol. 183, No. 2, 01.02.2007, p. 215-239.

Research output: Contribution to journalReview article

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