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Justification of diffusion limit for the Boltzmann equation with a non-trivial profile

Feimin Huang Yi Wang Yong Wang Tong Yang

Analysis of PDEs mathscidoc:1912.43764

arXiv preprint arXiv:1505.02258, 2015.5
Under the diffusion scaling and a scaling assumption on the microscopic component, a non-classical fluid dynamic system was derived in\cite {BGLY} that is related to the system of ghost effect derived in\cite {Sone-2} in different settings. This paper aims to justify this limit system for a non-trivial background profile with slab symmetry. The result reveals not only the diffusion phenomena in the temperature and density, but also the flow of higher order in Knudsen number due to the gradient of the temperature. Precisely, we show that the solution to the Boltzmann equation converges to a diffusion wave with decay rates in both Knudsen number and time.
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@inproceedings{feimin2015justification,
  title={Justification of diffusion limit for the Boltzmann equation with a non-trivial profile},
  author={Feimin Huang, Yi Wang, Yong Wang, and Tong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205617520707328},
  booktitle={arXiv preprint arXiv:1505.02258},
  year={2015},
}
Feimin Huang, Yi Wang, Yong Wang, and Tong Yang. Justification of diffusion limit for the Boltzmann equation with a non-trivial profile. 2015. In arXiv preprint arXiv:1505.02258. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205617520707328.
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