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

TL;DR

This paper establishes local well-posedness and blow-up criteria for a two-component Novikov system in critical Besov spaces, advancing understanding of the system's behavior in these function spaces.

Contribution

It proves local well-posedness in Besov spaces and introduces blow-up criteria for the two-component Novikov system, especially in critical Besov spaces.

Findings

Well-posedness in Besov spaces $B^{s-1}_{p,r} imes B^s_{p,r}$ for $s > ext{max}igrace 1+rac{1}{p}, rac{3}{2} igrace$

Local well-posedness in critical Besov space $B^{1/2}_{2,1} imes B^{3/2}_{2,1}$

Two blow-up criteria based on conservation laws

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 $B^{s-1}_{p,r}\times B^s_{p,r}$ 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 $B^{\frac{1}{2}}_{2,1}\times B^{\frac{3}{2}}_{2,1}$. Moreover, we present two blow-up criteria for the system by making use of the conservation laws.