The local well-posedness and existence of weak solutions for a generalized Camassa–Holm equation

Abstract

A generalization of the Camassa–Holm equation, a model for shallow water waves, is investigated. Using the pseudoparabolic regularization technique, its local well-posedness in Sobolev space H s ( R ) with s > 3 2 is established via a limiting procedure. In addition, a sufficient condition for the existence of weak solutions of the equation in lower order Sobolev space H s with 1 < s ⩽ 3 2 is developed.