Conservative solutions of the Camassa-Holm Equation on the real line

Abstract

In this paper we construct a global, continuous flow of solutions to the Camassa-Holm equation on the space H1(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.