  We show that in bounded domains with no-slip boundary conditions, the
Navier-Stokes pressure can be determined in a such way that it is strictly
dominated by viscosity. As a consequence, in a general domain we can treat the
Navier-Stokes equations as a perturbed vector diffusion equation, instead of as
a perturbed Stokes system. To illustrate the advantages of this view, we
provide a simple proof of the unconditional stability of a difference scheme
that is implicit only in viscosity and explicit in both pressure and convection
terms, requiring no solution of stationary Stokes systems or inf-sup
conditions.
