@article {2005,
title = {An Optimal Transportation Metric for Solutions of the Camassa-Holm Equation},
number = {SISSA;27/2005/M},
year = {2005},
abstract = {In this paper we construct a global, continuous flow of solutions to the Camassa-Holm equation on the entire space H1. Our solutions are conservative, in the sense that the total energy int[(u2 + u2x) dx] remains a.e. constant in time. Our new approach is based on a distance functional J(u, v), defined in terms of an optimal transportation problem, which satisfies d dtJ(u(t), v(t)) <= κ {\textperiodcentered} J(u(t), v(t)) for every couple of solutions. Using this new distance functional, we can construct arbitrary solutions as the uniform limit of multi-peakon solutions, and prove a general uniqueness result.},
url = {http://hdl.handle.net/1963/1719},
author = {Alberto Bressan and Massimo Fonte}
}