  We consider some complex-valued solutions of the Navier-Stokes equations in
$R^{3}$ for which Li and Sinai proved a finite time blow-up. We show that there
are two types of solutions, with different divergence rates, and report results
of computer simulations, which give a detailed picture of the blow-up for both
types. They reveal in particular important features not, as yet, predicted by
the theory, such as a concentration of the energy and the enstrophy around a
few singular points, while elsewhere the "fluid" remains quiet.
