Numerical verification of regularity in the three-dimensional Navier-Stokes equations for bounded sets of initial data

|curlu0| ) is sufficiently small, ‖Du0‖ 2 ≤ χ0. 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, ‖Du0‖ 2 ≤ χ1. Under the assumption that the equations are in fact regular we show that this procedure can be guaranteed to terminate after a finite time.