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Global existence to Boltzmann equation with external force in infinite vacuum

Renjun Duan Tong Yang Changjiang Zhu

Analysis of PDEs mathscidoc:1912.43965

Journal of mathematical physics, 46, (5), 053307, 2005.5
In this paper, we give a condition on the bicharacteristic which guarantees the global existence of the mild solution to the Boltzmann equation with an external force for the hard-sphere model and potentials with angular cutoff in infinite vacuum. This generalizes the previous results to the case when the force can have arbitrary strength. The constructive condition on the bicharacteristic is used to obtain the pointwise estimates on the collision operator so that the global existence comes from the contraction mapping theorem.
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@inproceedings{renjun2005global,
  title={Global existence to Boltzmann equation with external force in infinite vacuum},
  author={Renjun Duan, Tong Yang, and Changjiang Zhu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210942994491529},
  booktitle={Journal of mathematical physics},
  volume={46},
  number={5},
  pages={053307},
  year={2005},
}
Renjun Duan, Tong Yang, and Changjiang Zhu. Global existence to Boltzmann equation with external force in infinite vacuum. 2005. Vol. 46. In Journal of mathematical physics. pp.053307. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210942994491529.
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