Periodic conservative solutions of the Camassa-Holm equation

We show that the periodic Camassa-Holm equation u(t) - u(xxt) + 3uu(x)-2u(x)u(xx)-uu(xxx) = 0 possesses a global continuous semigroup of weak conservative solutions for initial data u vertical bar(t=0) in H-per(1). The result is obtained by introducing per a coordinate transformation into Lagrangian coordinates. To characterize conservative solutions it is necessary to include the energy density given by the positive Radon measure mu with mu(ac), = (u(2) + u(x)(2))dx. The total energy is preserved by the solution.