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Optimal decay estimates on the linearized Boltzmann equation with time dependent force and their applications

Renjun Duan Seiji Ukai Tong Yang Huijiang Zhao

Analysis of PDEs mathscidoc:1912.43937

Communications in Mathematical Physics, 277, (1), 189-236, 2008.1
Although the decay in time estimates of the semi-group generated by the linearized Boltzmann operator without forcing have been well established, there is no corresponding result for the case with general external force. This paper is mainly concerned with the optimal decay estimates on the solution operator in some weighted Sobolev spaces for the linearized Boltzmann equation with a time dependent external force. No time decay assumption is made on the force. The proof is based on both the energy method through the macro-micro decomposition and the <i>L</i> <sup> <i>p</i> </sup>-<i>L</i> <sup> <i>q</i> </sup> estimates from the spectral analysis. The decay estimates thus obtained are applied to the study on the global existence of the Cauchy problem to the nonlinear Boltzmann equation with time dependent external force and source. Precisely, for space dimension <i>n</i>3, the
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@inproceedings{renjun2008optimal,
  title={Optimal decay estimates on the linearized Boltzmann equation with time dependent force and their applications},
  author={Renjun Duan, Seiji Ukai, Tong Yang, and Huijiang Zhao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210753030226501},
  booktitle={Communications in Mathematical Physics},
  volume={277},
  number={1},
  pages={189-236},
  year={2008},
}
Renjun Duan, Seiji Ukai, Tong Yang, and Huijiang Zhao. Optimal decay estimates on the linearized Boltzmann equation with time dependent force and their applications. 2008. Vol. 277. In Communications in Mathematical Physics. pp.189-236. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210753030226501.
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