Conservative solution of the Camassa Holm Equation on the real line

Details Conservative solution of the Camassa Holm Equation on the real line Conservative solution of the Camassa Holm Equation on the real line

2005-11-22

arxiv.org/abs/math/0511549v1

Mathematics

Analysis of PDEs

15 pages, 2 figures

Scientific paper

In this paper we construct a global, continuous flow of solutions to the Camassa-Holm equation on the space H^1(R). In a previous paper [2], A. Bressan and the author constructed spatially periodic solutions, whereas in this paper the solutions are defined in all the real line. We introduce a distance functional, defined in terms of an optimal transportation problem, which allows us to study the continuous dependance w.r.t. the inital data with a certain decay at infinity.

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