The Local and Global Existence of Solutions for a Generalized Camassa-Holm Equation - Nan Li; Shaoyong Lai; Shuang Li; Meng Wu (Abstract and Applied Analysis)
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 HS(R) with s>3/2 is established via a limiting procedure. Provided that the initial value u0 satisfies the sign condition and u0∈Hs(R)  (s>3/2), it is shown that there exists a unique global solution for the equation in space C([0,∞);Hs(R))∩C1([0,∞);Hs−1(R)).