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 $1\leq p, r\leq +\infty$ and $s>{\rm max}\{1+\frac{1}{p},\frac{3}{2}\}$. 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.