Local Well-posedness and Persistence Property for the Generalized Novikov Equation

Abstract

In this paper, we study the generalized Novikov equation which describesthe motion of shallow water waves. By using the Littlewood-Paleydecomposition and nonhomogeneous Besov spaces, we prove that the Cauchyproblem for the generalized Novikov equation is locally well-posedin 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 showthe persistence property of the strong solutions which implies thatthe solution decays at infinity in the spatialvariable provided that the initial function does.