  In this paper we mainly study the Cauchy problem for a generalized
Camassa-Holm equation. First, by using the Littlewood-Paley decomposition and
transport equations theory, we establish the local well-posedness for the
Cauchy problem of the equation in Besov spaces. Then we give a simply blow-up
criterion for the Cauchy problem of the equation. we present a blow-up result
and the exact blow-up rate of strong solutions to the equation by making use of
the conservation law and the obtained blow-up criterion.Finally, we verify that
the system possesses peakon solutions.
