00982nas a2200109 4500008004300000245008000043210006900123520060400192100002100796700001900817856003600836 2005 en_Ud 00aAn Optimal Transportation Metric for Solutions of the Camassa-Holm Equation0 aOptimal Transportation Metric for Solutions of the CamassaHolm E3 aIn 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 · 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.1 aBressan, Alberto1 aFonte, Massimo uhttp://hdl.handle.net/1963/1719