The Cauchy problem for the modified Novikov equation

Abstract

In this paper, we are concerned with the Cauchy problem for the modified Novikov equation. By using the transport equation theory and Littlewood-Paley decomposition as well as nonhomogeneous Besov spaces, we prove that the Cauchy problem for the modified Novikov equation is locally well posed in the Besov space B s p,r with 1 ≤ p, r ≤ +∞ and s > max{1 + 1 p , 3 2 } and show that the Cauchy problem for the modified Novikov equation is locally well posed in the Besov space B 3/2 2,1 with the aid of Osgood lemma.