  Current theoretical results for the three-dimensional Navier--Stokes
equations only guarantee that solutions remain regular for all time when the
initial enstrophy ($\|Du_0\|^2:=\int|{\rm curl} u_0|^2$) is sufficiently small,
  $\|Du_0\|^2\le\chi_0$. In fact, this smallness condition is such that the
enstrophy is always non-increasing. In this paper we provide a numerical
procedure that will verify regularity of solutions for any bounded set of
initial conditions,
  $\|Du_0\|^2\le\chi_1$. Under the assumption that the equations are in fact
regular we show that this procedure can be guaranteed to terminate after a
finite time.
