Electron. J. Differential Equations, Vol. 2021 (2021), No. 46, pp. 1-21.

Asymptotic behavior of linearized Boltzmann equations for soft potentials with cut-off

Yakui Wu, Jiawei Sun

Abstract:
We consider the asymptotic behavior of the linearized Boltzmann equation for soft potentials with cut-off. By introducing a new decomposition of the linearized Boltzmann operator, we analyze the spectrum of the linearized Boltzmann operator and obtain the asymptotic behaviors of the linearized Boltzmann equation for γ in (-3,0), extending the result in [12] for γ in (-1,0).

Submitted December 9, 2020. Published May 27, 2021.
Math Subject Classifications: 76P05, 35B20, 35B40, 35P20.
Key Words: Linearized Boltzmann operator; soft potentials; spectrum; semigroup; time decay; estimates.
DOI: https://doi.org/10.58997/ejde.2021.46

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Yakui Wu
School of Mathematical Sciences
Capital Normal University
Beijing 100048, China
email: 6070010@jju.edu.cn
Jiawei Sun
Department of Mathematics
Shandong Normal University
Jinan 250014, China
email: sunjiawei0122@163.com

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