The local strong and weak solutions for a nonlinear dissipative Camassa-Holm equation (Q642698)

Summary: Using the Kato theorem for abstract differential equations, the local well-posedness of the solution for a nonlinear dissipative Camassa-Holm equation is established in space \(C([0, T), H^s(R)) \cap C^1([0, T), H^{s-1}(R))\) with \(s > 3/2\). In addition, a sufficient condition for the existence of weak solutions of the equation in lower order Sobolev space \(H^s(R)\) with \(1 \leq s \leq 3/2\) is developed.