Global conservative solutions of the Camassa-Holm equation

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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.


  • Alberto Bressan
  • Adrian Constantin
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics
Original languageEnglish
Pages (from-to)215-239
JournalArchive for Rational Mechanics and Analysis
Issue number2
Publication statusPublished - 2007
Publication categoryResearch