摘要：In this paper, we study the Cauchy problem of a generalized Camassa-Holm equation. It is shown that the equation is locally well posed when the initial data are sufficiently smooth. Moreover, we present a sufficient condition which guarantees the existence of low regularity solutions for the generalized Camassa-Holm equation by the method of energy estimate. Finally, the nonexistence of smooth solitary-wave solutions is investigated. MSC:35Q51, 35Q53, 35B35.
