Archive for Rational Mechanics and Analysis

, Volume 183, Issue 2, pp 215–239

Global Conservative Solutions of the Camassa–Holm Equation


DOI: 10.1007/s00205-006-0010-z

Cite this article as:
Bressan, A. & Constantin, A. Arch Rational Mech Anal (2007) 183: 215. doi:10.1007/s00205-006-0010-z


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.

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of MathematicsPennsylvania State UniversityUniversity ParkU.S.A.
  2. 2.School of MathematicsTrinity College DublinDublin 2Ireland
  3. 3.Department of MathematicsLund UniversityLundSweden