数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (6): 1487-1507.doi: 10.1007/s10473-019-0602-y

• 论文 • 上一篇    下一篇

SHUBIN REGULARITY FOR THE RADIALLY SYMMETRIC SPATIALLY HOMOGENEOUS BOLTZMANN EQUATION WITH DEBYE-YUKAWA POTENTIAL

Léo GLANGETAS1, 李浩光2   

  1. 1. Université de Rouen, CNRS UMR 6085, Mathématiques 76801 Saint-Etienne du Rouvray, France;
    2. School of Mathematics and Statistics, South-central University for Nationalities, Wuhan 430074, China
  • 收稿日期:2018-08-30 修回日期:2019-05-09 出版日期:2019-12-25 发布日期:2019-12-30
  • 通讯作者: Haoguang LI,E-mail:lihaoguang@mail.scuec.edu.cn E-mail:lihaoguang@mail.scuec.edu.cn
  • 作者简介:Léo GLANGETAS,E-mail:leo.glangetas@univ-rouen.fr
  • 基金资助:
    The research of the second author was supported by the Natural Science Foundation of China (11701578).

SHUBIN REGULARITY FOR THE RADIALLY SYMMETRIC SPATIALLY HOMOGENEOUS BOLTZMANN EQUATION WITH DEBYE-YUKAWA POTENTIAL

Léo GLANGETAS1, Haoguang LI2   

  1. 1. Université de Rouen, CNRS UMR 6085, Mathématiques 76801 Saint-Etienne du Rouvray, France;
    2. School of Mathematics and Statistics, South-central University for Nationalities, Wuhan 430074, China
  • Received:2018-08-30 Revised:2019-05-09 Online:2019-12-25 Published:2019-12-30
  • Contact: Haoguang LI,E-mail:lihaoguang@mail.scuec.edu.cn E-mail:lihaoguang@mail.scuec.edu.cn
  • Supported by:
    The research of the second author was supported by the Natural Science Foundation of China (11701578).

摘要: In this work, we study the Cauchy problem for the radially symmetric spatially homogeneous Boltzmann equation with Debye-Yukawa potential. We prove that this Cauchy problem enjoys the same smoothing effect as the Cauchy problem defined by the evolution equation associated to a fractional logarithmic harmonic oscillator. To be specific, we can prove the solution of the Cauchy problem belongs to Shubin spaces.

关键词: Boltzmann equation, shubin regularity, spectral decomposition, Debye-Yukawa potential

Abstract: In this work, we study the Cauchy problem for the radially symmetric spatially homogeneous Boltzmann equation with Debye-Yukawa potential. We prove that this Cauchy problem enjoys the same smoothing effect as the Cauchy problem defined by the evolution equation associated to a fractional logarithmic harmonic oscillator. To be specific, we can prove the solution of the Cauchy problem belongs to Shubin spaces.

Key words: Boltzmann equation, shubin regularity, spectral decomposition, Debye-Yukawa potential

中图分类号: 

  • 35Q20