Preprint 2005-016

Global Conservative Solutions of the Camassa–Holm Equation

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.

Paper:

Available as PDF (216 Kbytes).

Author(s):

Alberto Bressan, <bressan@math.psu.edu>

Adrian Constantin, <adrian.constantin@math.lu.se>

Publishing information:

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Submitted by:

<adrian.constantin@math.lu.se> April 14 2005.