Global conservative solutions of the Camassa-Holm equation

Alberto Bressan, Adrian Constantin

Research output: Contribution to journalReview articlepeer-review

546 Scopus citations

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 2007

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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