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

Abstract 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 B p , r s − 1 × B p , r s with p , r ∈ [ 1 , ∞ ] , s > max { 1 + 1 p , 3 2 } 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 B 2 , 1 1 2 × B 2 , 1 3 2 . Moreover, we present two blow-up criteria for the system by making use of the conservation laws.