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

A fully nonlinear generalization of the Camassa-Holm equation is investigated. Using the pseudoparabolic regularization technique, its local well-posedness in Sobolev space H s(.) with s>32 is established via a limiting procedure. Provided that the initial momentum (1 -. 2x)u 0 satisfies the sign condition, u 0 . H s(.)(s>32) and u 0 . L 1(.), the existence and uniqueness of global solutions for the equation are shown to be true in the space C([0,.);H s(.)) . C 1([0,g8);H s.1(.))