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 admin note: text overlap with arXiv:1505.00086

References in corpus (4)

• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• On an integrable two-component Camassa-Holm shallow water system
• Singular solutions of a modified two-component Camassa-Holm equation
• Double Extended Cubic Peakon Equation