A half-space problem for the Boltzmann equation with specular reflection boundary condition

Tong Yang Hui-Jiang Zhao

Analysis of PDEs mathscidoc:1912.43966

Communications in mathematical physics, 255, (3), 683-726, 2005.4
There are many open problems on the stability of nonlinear wave patterns to the Boltzmann equation even though the corresponding stability theory has been comparatively well-established for the gas dynamical systems. In this paper, we study the nonlinear stability of a rarefaction wave profile to the Boltzmann equation with the boundary effect imposed by specular reflection for both the hard sphere model and the hard potential model with angular cut-off. The analysis is based on the property of the solution and its derivatives which are either odd or even functions at the boundary coming from specular reflection, and the decomposition on both the solution and the Boltzmann equation introduced in [24, 26] for energy method.
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@inproceedings{tong2005a,
  title={A half-space problem for the Boltzmann equation with specular reflection boundary condition},
  author={Tong Yang, and Hui-Jiang Zhao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210946164320530},
  booktitle={Communications in mathematical physics},
  volume={255},
  number={3},
  pages={683-726},
  year={2005},
}
Tong Yang, and Hui-Jiang Zhao. A half-space problem for the Boltzmann equation with specular reflection boundary condition. 2005. Vol. 255. In Communications in mathematical physics. pp.683-726. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210946164320530.
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