L1 and BV-type stability of the Boltzmann equation with external forces

Renjun Duan Tong Yang Changjiang Zhu

Analysis of PDEs mathscidoc:1912.43957

Journal of Differential Equations, 227, (1), 1-28, 2006.8
Based on the existence theory on the Boltzmann equation with external forces in infinite vacuum, in this paper, we will study the L1 and BV-type stability of the classical solutions for small initial data. The stability results generalize those for the Boltzmann equation without force to the case with external force. In particular, we show that the stability can be established for the soft potentials directly, while the stability for the hard potentials and hard sphere model is obtained through the construction of some nonlinear functionals. The functionals thus constructed generalize those constructed in [S.-Y. Ha, Nonlinear functionals of the Boltzmann equation and uniform stability estimates, J. Differential Equations 215 (2005) 178205] for the case without force to capture the effect of the force term on the time evolution of the solutions. 2006 Elsevier Inc. All rights reserved.
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@inproceedings{renjun2006l1,
  title={L1 and BV-type stability of the Boltzmann equation with external forces},
  author={Renjun Duan, Tong Yang, and Changjiang Zhu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210911288354521},
  booktitle={Journal of Differential Equations},
  volume={227},
  number={1},
  pages={1-28},
  year={2006},
}
Renjun Duan, Tong Yang, and Changjiang Zhu. L1 and BV-type stability of the Boltzmann equation with external forces. 2006. Vol. 227. In Journal of Differential Equations. pp.1-28. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210911288354521.
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