The local and global existence of solutions for a generalized Camassa-Holm equation (Q5891549)

Summary: A nonlinear generalization of the Camassa-Holm equation is investigated. By making use of the pseudoparabolic regularization technique, its local well posedness in Sobolev space \(H^s(\mathbb{R})\) with \(s > 3/2\) is established via a limiting procedure. Provided that the initial value \(u_0\) satisfies the sign condition and \(u_0 \in H^s (\mathbb{R})\) (\(s > 3/2\)), it is shown that there exists a unique global solution for the equation in space \(C([0, \infty); H^s(\mathbb{R})) \cap C^1([0, \infty); H^{s-1}(\mathbb{R}))\).