  We show that t^{3/4}|| u(.,t) ||_{sup} --> 0 as t --> infty for all (global)
Leray solutions of the incompressible Navier-Stokes equations in R3. It is also
shown that t || u(.,t) - v(.,t) ||_{sup} --> 0 as t --> infty, where v(.,t) is
the Stokes approximation, as well as other fundamental results. In spite of the
difficulty of these questions, our approach is elementary and is based on
standard tools like conventional Fourier and energy methods.
