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Kinetic and viscous boundary layers for the Broadwell equations

Jian-Guo Liu Temple University Zhouping Xin Courant Institute

Analysis of PDEs mathscidoc:1702.03071

Transport Theory and Statistical Physics, 25, (3), 447-461, 1996.4
In this paper, we investigate the boundary layer behavior of solutions to the one dimensional Broadwell model of the nonlinear Boltzmann equation for small mean free path. We consider the analogue of Maxwell's diffusive and the reflexive boundary conditions. It is found that even for such a simple model, there are boundary layers due to purely kinetic effects which cannot be detected by the corresponding Navier-Stokes system. It is also found numerically that a compressive boundary layer is not always stable in the sense that it may detach from the boundary and move into the interior of the gas as a shock layer.
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@inproceedings{jian-guo1996kinetic,
  title={Kinetic and viscous boundary layers for the Broadwell equations},
  author={Jian-Guo Liu, and Zhouping Xin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209131825302718401},
  booktitle={Transport Theory and Statistical Physics},
  volume={25},
  number={3},
  pages={447-461},
  year={1996},
}
Jian-Guo Liu, and Zhouping Xin. Kinetic and viscous boundary layers for the Broadwell equations. 1996. Vol. 25. In Transport Theory and Statistical Physics. pp.447-461. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209131825302718401.
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