Non-uniform continuous dependence on initial data for a two_component Novikov system in Besov space

Abstract

In this paper, we show that the solution map of the two-component Novikov system is not uniformly continuous on the initial data in Besov spaces $B_{p,r}^{s-1}(\mathbb{R})\times B_{p,r}^s(\mathbb{R})$ with $s>\max \{1+\frac{1}{p},\frac{3}{2}\}$, $1\le p<\infty$, $1\le r<\infty$. Our result covers and extends the previous non-uniform continuity in Sobolev spaces $H^{s-1}(\mathbb{R})\times H^s(\mathbb{R})$ for $s>\frac{5}{2}$ (J. Math. Phys., 2017) to Besov spaces.

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