Global well-posedness of the Boltzmann equation with large amplitude initial data

Renjun Duan Feimin Huang Yong Wang Tong Yang

Analysis of PDEs mathscidoc:1912.43979

Archive for Rational Mechanics and Analysis, 225, (1), 375-424, 2017.7
The global well-posedness of the Boltzmann equation with initial data of large amplitude has remained a long-standing open problem. In this paper, by developing a new L x L v 1 L x , v approach, we prove the global existence and uniqueness of mild solutions to the Boltzmann equation in the whole space or torus for a class of initial data with bounded velocity-weighted L x L v 1 L x , v norm under some smallness condition on the L x L v 1 L x , v norm as well as defect mass, energy and entropy so that the initial data allow large amplitude oscillations. Both the hard and soft potentials with angular cut-off are considered, and the large time behavior of solutions in the L x L v 1 L x , v norm with explicit rates of convergence are also studied.
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@inproceedings{renjun2017global,
  title={Global well-posedness of the Boltzmann equation with large amplitude initial data},
  author={Renjun Duan, Feimin Huang, Yong Wang, and Tong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211028715428543},
  booktitle={Archive for Rational Mechanics and Analysis},
  volume={225},
  number={1},
  pages={375-424},
  year={2017},
}
Renjun Duan, Feimin Huang, Yong Wang, and Tong Yang. Global well-posedness of the Boltzmann equation with large amplitude initial data. 2017. Vol. 225. In Archive for Rational Mechanics and Analysis. pp.375-424. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211028715428543.
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