Energy of wave and solutions of C-Holm equation under Lagrangian point of view

     Abstract:

We deal with the Camassa-Holm equation   possesses a global continuous semigroup of weak conservative solutions for initial data. The result is obtained by introducing a coordinate transformation into Lagrangian coordinates. To characterize conservative solutions it is necessary to include the energy density given by the positive Radon measure µ with . The total energy is preserved by the solution.