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Multi-scale nonlinear singular limit for thermal non-equilibrium gas flow with multiple non-equilibrium modes for analytic data in multi-dimensions with physical boundaries

Tao Luo Department of Mathematics, City University of Hong Kong, Kowloon Tong, Hong Kong SAR, China Yan-Lin Wang YMSC, Tsinghua University, Beijing, China

Analysis of PDEs mathscidoc:2204.03005

Journal of Mathematics Physics, 61, 101512, 2020.10
The multi-scale zero relaxation singular limit for gas dynamics in thermal non-equilibrium with multiple non-equilibrium modes in multi-dimensions with physical boundaries from non-equilibrium to thermal equilibrium of compressible Euler flow is proved in this paper for analytical data by establishing the uniform local-in-time estimates. A cancellation mechanism is utilized to deal with the nonlinear singular terms that cause the increase in both time and space derivatives in energy estimates. The rates of the relaxations corresponding to different non-equilibrium modes tending to zero discussed in this paper can be arbitrarily different.
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@inproceedings{tao2020multi-scale,
  title={Multi-scale nonlinear singular limit for thermal non-equilibrium gas flow with multiple non-equilibrium modes for analytic data in multi-dimensions with physical boundaries},
  author={Tao Luo, and Yan-Lin Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220428131212085421133},
  booktitle={Journal of Mathematics Physics},
  volume={61},
  pages={101512},
  year={2020},
}
Tao Luo, and Yan-Lin Wang. Multi-scale nonlinear singular limit for thermal non-equilibrium gas flow with multiple non-equilibrium modes for analytic data in multi-dimensions with physical boundaries. 2020. Vol. 61. In Journal of Mathematics Physics. pp.101512. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220428131212085421133.
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