  A modified version of the three dimensional Navier-Stokes equations is
considered with periodic boundary conditions. A bounded constant delay is
introduced into the convective term, that produces a regularizing effect on the
solution. In fact, by assuming appropriate regularity on the initial data, the
solutions of the delayed equations are proved to be regular and, as a
consequence, existence and also uniqueness of a global weak solution is
obtained. Moreover, the associated flow is constructed and the continuity of
the semigroup is proved. Finally, we investigate the passage to the limit on
the delay, obtaining that the limit is a weak solution of the Navier-Stokes
equations.
