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On incompressible Navier-Stokes dynamics: a new approach for analysis and computation

Jian-Guo Liu University of Maryland Jie Liu University of Maryland Robert L. Pego Carnegie Mellon University

Analysis of PDEs mathscidoc:1702.03061

2006.1
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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@inproceedings{jian-guo2006on,
  title={On incompressible Navier-Stokes dynamics: a new approach for analysis and computation},
  author={Jian-Guo Liu, Jie Liu, and Robert L. Pego},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209091834579514362},
  year={2006},
}
Jian-Guo Liu, Jie Liu, and Robert L. Pego. On incompressible Navier-Stokes dynamics: a new approach for analysis and computation. 2006. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209091834579514362.
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