  We give a construction of a divergence-free vector field $u_0 \in H^s \cap
B^{-1}_{\infty,\infty}$, for all $s<1/2$, such that any Leray-Hopf solution to
the Navier-Stokes equation starting from $u_0$ is discontinuous at $t=0$ in the
metric of $B^{-1}_{\infty,\infty}$. For the Euler equation a similar result is
proved in all Besov spaces $B^s_{r,\infty}$ where $s>0$ if $r>2$, and
$s>n(2/r-1)$ if $1 \leq r \leq 2$.
