The Cauchy problem for a generalized Dullin–Gottwald–Holm equation in Besov spaces

Abstract

This paper deals with the Cauchy problem for a generalized Dullin–Gottwald–Holm (DGH) equation. The local well-posedness of the generalized DGH equation is obtained in Besov space with and by the transport equations theory and the classical Friedrichs regularization method. Moreover, the local well-posedness in critical case is also considered. Then a lower bound for the maximal existence time of the solution is derived. Finally, the analytic of the solution is given.