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On Incompressible Navier-Stokes Dynamics: A New Approach for Analysis and Computation

Jian-Guo Liu·Jie Liu·Robert L. Pego
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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 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.

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Jian-Guo Liu, Jie Liu, Robert L. Pego. 2005-03-11. On Incompressible Navier-Stokes Dynamics: A New Approach for Analysis and Computation. https://arxiv.org/abs/math/0503212

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