Ill-posedness for the higher dimensional Camassa-Holm equations in Besov spaces

In the paper, by constructing a initial data $u_{0}in B^{sigma}_{p,infty}$ with $sigma-2>max{1+frac 1 p, frac 3 2}$, we prove that the corresponding solution to the higher dimensional Camassa-Holm equations starting from $u_{0}$ is discontinuous at $t=0$ in the norm of $B^{sigma}_{p,infty}$, which implies that the ill-posedness for the higher dimensional Camassa-Holm equations in $B^{sigma}_{p,infty}$.