The existence and uniqueness of the local solution for a Camassa–Holm type equation

摘要

A shallow water equation of Camassa–Holm type, containing nonlinear dissipative effect, is investigated. Using the techniques of the pseudoparabolic regularization and some prior estimates derived from the equation itself, we establish the existence and uniqueness of its local solution in Sobolev space Hs(R) with s>32. Meanwhile, a new lemma and a sufficient condition which guarantee the existence of solutions of the equation in lower order Sobolev space Hs with 1