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Global Conservative Solutions of the Camassa–Holm Equation

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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.

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Authors and Affiliations

  1. Department of Mathematics, Pennsylvania State University, University Park, 16802, U.S.A.

    Alberto Bressan

  2. School of Mathematics, Trinity College Dublin, Dublin 2, Ireland

    Adrian Constantin

  3. Department of Mathematics, Lund University, 22100, Lund, Sweden

    Adrian Constantin

Authors
  1. Alberto Bressan
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  2. Adrian Constantin
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Correspondence to Alberto Bressan.

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Bressan, A., Constantin, A. Global Conservative Solutions of the Camassa–Holm Equation. Arch Rational Mech Anal 183, 215–239 (2007). https://doi.org/10.1007/s00205-006-0010-z

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  • DOI: https://doi.org/10.1007/s00205-006-0010-z

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