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 $B_{p,r}^{s-1}\times B_{p,r}^s$ with $p,r\in [1,\infty ],s>\max \{1+\frac{1}{p},\frac{3}{2}\}$ 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 $B_{2,1}^{\frac{1}{2}}\times B_{2,1}^{\frac{3}{2}}$. Moreover, we present two blow-up criteria for the system by making use of the conservation laws.

arXiv commentarXiv admin note: text overlap with arXiv:1505.00086

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Cited by in corpus (2)

• Local well-posedness and blow-up for a family of $U(1)$-invariant peakon equations
• Blow-up phenomena and local well-posedness for a generalized Camassa-Holm equation