Ill-posedness issue on the Oldroyd-B model in the critical Besov spaces

It is proved in \cite[J. Funct. Anal., 2020]{AP} that the Cauchy problem for some Oldroyd-B model is well-posed in ${\text{B}}_{p,1}^{d\mathrm{/}p-1}({\mathbb{R}}^d)\times {\text{B}}_{p,1}^{d\mathrm{/}p}({\mathbb{R}}^d)$ with $1\le p<2d$. In this paper, we prove that the Cauchy problem for the same Oldroyd-B model is ill-posed in ${\text{B}}_{p,r}^{d\mathrm{/}p-1}({\mathbb{R}}^d)\times {\text{B}}_{p,r}^{d\mathrm{/}p}({\mathbb{R}}^d)$ with $1\le p\le \mathrm{\infty }$ and $1<r\le \mathrm{\infty }$ due to the lack of continuous dependence of the solution.