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{\bf \large Divorcing Pressure from Viscosity in Incompressible Navier-Stokes Dynamics} 

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Jian-Guo Liu\\
Departent of Mathematics \& Institute for Physical Scinece and Technology\\
University of Maryland\\
College Park, MD  20742\\
jliu@math.umd.edu 

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Jie Liu\\
Department of mathematics\\
University of maryland\\
College Park, MD 20742\\
jieliu@math.umd.edu

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and\\

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Robert L. Pego\\
Department of Mathematical Sciences\\
Carnegie Mellon Univeristy\\
Pittsburgh, PA  15213\\
rpego@cmu.edu

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\noindent {\bf Abstract}: 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 perturbed vector diffusion equation, instead of as a
perturbed Stokes system.  We illustrate the advantages of this view in
a number of ways.  In particular, we provide simple proofs of (i)
local-in-time existence and uniqueness of strong solutions for an
unconsrained formulation of the Navier-Stokes equations, and (ii) the
unconditional stability and convergence of difference schemes that are
implicit only in viscosity and explicit in both pressure and
convection terms, requiring no solution of stationary Stokes systems
or inf-sup conditions.

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