Local well-posedness and persistence property for the generalized Novikov equation

In this paper, we study the generalized Novikov equation which describes the motion of shallow water waves. By using the Littlewood-Paley decomposition and nonhomogeneous Besov spaces, we prove that the Cauchy problem for the generalized Novikov equation is locally well-posed in Besov space B-p,r(s) with 1 <= p,r <= +infinity and s > max {1 + 1/p, 3/2}. We also show the persistence property of the strong solutions which implies that the solution decays at infinity in the spatial variable provided that the initial function does.