On Incompressible Navier-Stokes Dynamics: A New Approach for Analysis   and Computation
  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. 
Jian-Guo Liu (1), Jie Liu (1), Robert L. Pego (2) ((1) University of   Maryland College Park, (2) Carnegie Mellon University)