数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (5): 1519-1539.doi: 10.1016/S0252-9602(14)60101-6

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THE NON-CUTOFF BOLTZMANN EQUATION WITH POTENTIAL FORCE IN THE WHOLE SPACE

雷远杰   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • 收稿日期:2013-03-13 修回日期:2013-05-20 出版日期:2014-09-20 发布日期:2014-09-20
  • 基金资助:

    This work was supported by the Fundamental Research Funds for the Central Universities.

THE NON-CUTOFF BOLTZMANN EQUATION WITH POTENTIAL FORCE IN THE WHOLE SPACE

 LEI Yuan-Jie   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2013-03-13 Revised:2013-05-20 Online:2014-09-20 Published:2014-09-20
  • Supported by:

    This work was supported by the Fundamental Research Funds for the Central Universities.

摘要:

This paper is concerned with the non-cutoff Boltzmann equation for full-range interactions with potential force in the whole space. We establish the global existence and optimal temporal convergence rates of classical solutions to the Cauchy problem when initial data is a small perturbation of the stationary solution. The analysis is based on the time-weighted energy method building also upon the recent studies of the non-cutoff Boltzmann equation in [1–3, 15] and the non-cutoff Vlasov-Poisson-Boltzmann system [6].

关键词: non-cutoff Boltzmann, potential force,  global existence, convergence rates

Abstract:

This paper is concerned with the non-cutoff Boltzmann equation for full-range interactions with potential force in the whole space. We establish the global existence and optimal temporal convergence rates of classical solutions to the Cauchy problem when initial data is a small perturbation of the stationary solution. The analysis is based on the time-weighted energy method building also upon the recent studies of the non-cutoff Boltzmann equation in [1–3, 15] and the non-cutoff Vlasov-Poisson-Boltzmann system [6].

Key words: non-cutoff Boltzmann, potential force,  global existence, convergence rates

中图分类号: 

  • 35A05