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arXiv · 1505.03992

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

Wei Luo·Zhaoyang Yin
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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.

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Wei Luo, Zhaoyang Yin. 2015-05-15. Local well-posedness and blow-up criteria for a two-component Novikov system in the critical Besov space. https://doi.org/10.1016/j.na.2015.03.022

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