Abstract: We show that the periodic Camassa–Holm equation u_t−u_xxt+3uu_x−2u_xu_xx−uu_xxx=0 possesses a global continuous semigroup of weak conservative solutions for initial data u|_t=0 in H¹_per. 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 μ_ac=(u²+u_x²)dx. The total energy is preserved by the solution.