数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (2): 459-476.doi: 10.1016/S0252-9602(15)60015-7

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CAUCHY PROBLEM FOR LINEARIZED NON-CUTOFF BOLTZMANN EQUATION WITH DISTRIBUTION INITIAL DATUM

李浩光   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • 收稿日期:2013-12-02 修回日期:2014-03-11 出版日期:2015-03-20 发布日期:2015-03-20
  • 基金资助:

    The research of this work was supported by the Fundamental Research Funds for the Central Unversities and National Science Foundation of China (11171261 and 11422106).

CAUCHY PROBLEM FOR LINEARIZED NON-CUTOFF BOLTZMANN EQUATION WITH DISTRIBUTION INITIAL DATUM

Haoguang LI   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2013-12-02 Revised:2014-03-11 Online:2015-03-20 Published:2015-03-20
  • Supported by:

    The research of this work was supported by the Fundamental Research Funds for the Central Unversities and National Science Foundation of China (11171261 and 11422106).

摘要:

In this article, we study the Cauchy problem for the linearized spatially homogeneous non-cutoff Boltzamnn equation with Maxwellian molecules. By using the spectral decomposition, we solve the Cauchy problem with initial datum in the sense of distribution, which contains the dual space of a Gelfand-Shilov class. We also prove that this solution belongs to the Gelfand-Shilov space for any positive time.

关键词: Boltzmann equation, spectral decomposition, Gelfand-Shilov class, distribution initial datum

Abstract:

In this article, we study the Cauchy problem for the linearized spatially homogeneous non-cutoff Boltzamnn equation with Maxwellian molecules. By using the spectral decomposition, we solve the Cauchy problem with initial datum in the sense of distribution, which contains the dual space of a Gelfand-Shilov class. We also prove that this solution belongs to the Gelfand-Shilov space for any positive time.

Key words: Boltzmann equation, spectral decomposition, Gelfand-Shilov class, distribution initial datum

中图分类号: 

  • 35Q20