Continuity of the data-to-solution map for the FORQ equation in Besov Spaces

For Besov spaces $B_{p,r}^s(\text{rr})$ with $s>\max \{2+\frac{1}{p},\frac{5}{2}\}$, $p\in (1,\mathrm{\infty }]$ and $r\in [1,\mathrm{\infty })$, it is proved that the data-to-solution map for the FORQ equation is not uniformly continuous from $B_{p,r}^s(\text{rr})$ to $C([0,T];B_{p,r}^s(\text{rr}))$. The proof of non-uniform dependence is based on approximate solutions and the Littlewood-Paley decomposition.