Preprint 2005-016

Global Conservative Solutions of the Camassa–Holm Equation

Alberto Bressan and Adrian Constantin

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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Alberto Bressan, <>
Adrian Constantin, <>
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<> April 14 2005.

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