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

2005/03/11 by Jian‐Guo Liu, Jie Liu, Liu, Jian-Guo +3
Computer Science · Engineering · Mathematics · #35Q30 #76D05 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.math/0503212

openalex publication_date 2005/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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