Abstract: We show that the Camassa–Holm equation
ut−uxxt+3uux-2uxuxx−uuxxx=0
possesses a global semigroup of weak conservative solutions. This is obtained by a change of variables corresponding to the transformation from Eulerian to Lagrangian coordinates. This approach enables us to define a non trivial complete metric which makes the semigroup of conservative solutions continuous. This is joint work with Helge Holden.