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Conservative solution of the Camassa Holm Equation on the real line

Research paper by Massimo Fonte

Indexed on: 22 Nov '05Published on: 22 Nov '05Published in: Mathematics - Analysis of PDEs



Abstract

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.