Local well-posedness and blow-up criteria for a two-component Novikov system in the critical Besov space

In this paper we mainly investigate the Cauchy problem of a two-component Novikov system. We first prove the local well-posedness of the system in Besov spaces Bp,rs−1×Bp,rs with p,r∈[1,∞],s>max{1+1p,32} by using the Littlewood–Paley theory and transport equations theory. Then, by virtue of logarithmic interpolation inequalities and the Osgood lemma, we establish the local well-posedness of the system in the critical Besov space B2,112×B2,132. Moreover, we present two blow-up criteria for the system by making use of the conservation laws.