  Given a finite sequence of times $0<t_1<...<t_N$, we construct an example of
a smooth solution of the free nonstationnary Navier--Stokes equations in
$\R^d$, $d=2,3$, such that: (i) The velocity field $u(x,t)$ is spatially poorly
localized at the beginning of the evolution but tends to concentrate until, as
the time $t$ approaches $t_1$, it becomes well-localized. (ii) Then $u$ spreads
out again after $t_1$, and such concentration-diffusion phenomena are later
reproduced near the instants $t_2$, $t_3$, ...
