  In the paper, we consider the Cauchy problem to the Euler equations in
$\mathbb{R}^d$ with $d\geq2$. We construct an initial data $u_0\in
B^\sigma_{p,\infty}$ showing that the corresponding solution map of the Euler
equations starting from $u_0$ is discontinuous at $t = 0$ in the metric of
$B^\sigma_{p,\infty}$, which implies the ill-posedness for this equation in
$B^\sigma_{p,\infty}$. We generalize the periodic result of Cheskidov and
Shvydkoy \cite{Cheskidov}.
