The Cauchy problem for the integrable Novikov equation

In this paper we consider the Cauchy problem for the integrable Novikov equation. By using the Littlewood-Paley decomposition and nonhomogeneous Besov spaces, we prove that the Cauchy problem for the integrable Novikov equation is locally well-posed in the Besov space B-p.r(s), with 1 <= p, r + infinity and s > max{1 + 1/p, 3/2} In particular, when u(0) is an element of B-p.r(s) boolean AND H-l with 1 <= p, r <= +infinity and s > max{1 + 1/p, 3/2}, for all t is an element of [0, T], we have that vertical bar vertical bar u(t)vertical bar vertical bar H-l = vertical bar vertical bar u(0)vertical bar vertical bar(H)l. We also prove that the local well-posedness of the Cauchy problem for the Novikov equation fails in B-2.(3/2)(infinity). (C) 2012 Elsevier Inc. All rights reserved.