数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (3): 857-888.doi: 10.1016/S0252-9602(18)30789-6

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STABILITY OF RAREFACTION WAVE FOR A MACROSCOPIC MODEL DERIVED FROM THE VLASOV-MAXWELL-BOLTZMANN SYSTEM

黄咏婷1, 刘红霞2   

  1. 1. Department of Mathematics, City University of Hong Kong, Hong Kong, China;
    2. Department of Mathematics, Jinan University, Guangzhou 510632, China
  • 收稿日期:2017-04-13 修回日期:2017-10-16 出版日期:2018-06-25 发布日期:2018-06-25
  • 通讯作者: Yongting HUANG E-mail:ythuang7-c@my.cityu.edu.hk
  • 作者简介:Hongxia LIU,E-mail:hongxia-liu@163.net
  • 基金资助:

    The second author is supported by the National Natural Science Foundation of China (11271160).

STABILITY OF RAREFACTION WAVE FOR A MACROSCOPIC MODEL DERIVED FROM THE VLASOV-MAXWELL-BOLTZMANN SYSTEM

Yongting HUANG1, Hongxia LIU2   

  1. 1. Department of Mathematics, City University of Hong Kong, Hong Kong, China;
    2. Department of Mathematics, Jinan University, Guangzhou 510632, China
  • Received:2017-04-13 Revised:2017-10-16 Online:2018-06-25 Published:2018-06-25
  • Contact: Yongting HUANG E-mail:ythuang7-c@my.cityu.edu.hk
  • Supported by:

    The second author is supported by the National Natural Science Foundation of China (11271160).

摘要:

In this article, we are concerned with the nonlinear stability of the rarefaction wave for a one-dimensional macroscopic model derived from the Vlasov-Maxwell-Boltzmann system. The result shows that the large-time behavior of the solutions coincides with the one for both the Navier-Stokes-Poisson system and the Navier-Stokes system. Both the timedecay property of the rarefaction wave profile and the influence of the electromagnetic field play a key role in the analysis.

关键词: Vlasov-Maxwell-Boltzmann system, rarefaction wave, energy method

Abstract:

In this article, we are concerned with the nonlinear stability of the rarefaction wave for a one-dimensional macroscopic model derived from the Vlasov-Maxwell-Boltzmann system. The result shows that the large-time behavior of the solutions coincides with the one for both the Navier-Stokes-Poisson system and the Navier-Stokes system. Both the timedecay property of the rarefaction wave profile and the influence of the electromagnetic field play a key role in the analysis.

Key words: Vlasov-Maxwell-Boltzmann system, rarefaction wave, energy method