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) (a"e) with is established via a limiting procedure. Provided that the initial momentum (1 -a, (x) (2) )u (0) satisfies the sign condition, u (0) a H (s) (a"e) and u (0) epsilon L (1)(a"e), the existence and uniqueness of global solutions for the equation are shown to be true in the space C([0,a);H (s) (a"e)) a (c) C (1)([0,g8);H (s-1)(a"e)).