The Local and Global Existence of Solutions for a Generalized Camassa-Holm Equation

Abstract EN

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)).