The Cauchy problem for a two-component Novikov equation in the critical Besov space

In this paper, we consider the Cauchy problem for a two-component Novikov equation in the critical Besov space B-2,1(5/2). We first derive a new a priori estimate for the 1-D transport equation in B-2,infinity(3/2) which is the endpoint case. Then we apply this a priori estimate and the Osgood lemma to prove the local existence. Moreover, we also show that the solution map no u(0) -> u is Holder continuous in B-2,1(5/2) equipped with weaker topology. It is worth mentioning that our method is different from the previous one that involves extracting a convergent subsequence from an iterative sequence in critical Besov spaces. (C) 2014 Elsevier Inc. All rights reserved.