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

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$s>\max{1+\frac{1}{p}, \frac{3}{2}}$,$1\leq p< \infty$,$1\leq r<\infty$. 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.