A note on the Camassa-Holm equation

We consider a generalized Camassa-Holm equation. We improve the compactness argument of [5-7,17], establishing the existence of global weak solutions in H1 without the use of an OleÄ­nik-type estimate. The potential interest of this improvement is linked to convergence analysis of numerical schemes, for which it may not be easy to verify an OleÄ­nik-type estimate.