Dissipative solutions for the Camassa–Holm equation
Helge Holden and Xavier Raynaud
Abstract: We show that the Camassa–Holm equation ut−uxxt+3uux−2uxuxx−uuxxx=0 possesses a global continuous semigroup of weak dissipative solutions for initial data u|t=0 in H1. The result is obtained by introducing a coordinate transformation into Lagrangian coordinates. Stability in terms of H1 and L∞ norm is discussed.