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Estimates on the Stokes pressure by partitioning the energy of harmonic functions

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

Analysis of PDEs mathscidoc:1702.03059

Rims Kokyuroku Bessatsu, 1, 251-270, 2007.3
We show that in a tubular domain with sufficiently small width, the normal and tangential gradients of a harmonic function have almost the same L 2 norm. This estimate yields a sharp estimate of the pressure in terms of the viscosity term in the Navier-Stokes equation with no-slip boundary condition. By consequence, one can analyze the Navier-Stokes equations simply as a perturbed vector diffusion equation instead of as a perturbed Stokes system. As an application, we describe a rather easy approach to establish a new isomorphism theorem for the non-homogeneous Stokes system.
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@inproceedings{jian-guo2007estimates,
  title={Estimates on the Stokes pressure by partitioning the energy of harmonic functions },
  author={Jian-Guo Liu, Jie Liu, and Robert L. Pego},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209085142415363358},
  booktitle={Rims Kokyuroku Bessatsu},
  volume={1},
  pages={251-270},
  year={2007},
}
Jian-Guo Liu, Jie Liu, and Robert L. Pego. Estimates on the Stokes pressure by partitioning the energy of harmonic functions . 2007. Vol. 1. In Rims Kokyuroku Bessatsu. pp.251-270. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209085142415363358.
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