数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (5): 2179-2203.doi: 10.1007/s10473-023-0515-7

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NONLINEAR STABILITY OF RAREFACTION WAVES TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS FOR A REACTING MIXTURE WITH ZERO HEAT CONDUCTIVITY*

Lishuang Peng, Yong Li   

  1. Faculty of Science, Beijing University of Technology, Beijing 100124, China
  • 收稿日期:2021-11-11 修回日期:2023-05-02 发布日期:2023-10-25

NONLINEAR STABILITY OF RAREFACTION WAVES TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS FOR A REACTING MIXTURE WITH ZERO HEAT CONDUCTIVITY*

Lishuang Peng, Yong Li   

  1. Faculty of Science, Beijing University of Technology, Beijing 100124, China
  • Received:2021-11-11 Revised:2023-05-02 Published:2023-10-25
  • Contact: †Yong Li, E-mail: yli@bjut.edu.cn
  • About author:Lishuang Peng, E-mail: penglishuang1@163.com
  • Supported by:
    Beijing Natural Science Foundation (1182004, Z180007, 1192001).

摘要: In this paper, we study the time-asymptotically nonlinear stability of rarefaction waves for the Cauchy problem of the compressible Navier-Stokes equations for a reacting mixture with zero heat conductivity in one dimension. If the corresponding Riemann problem for the compressible Euler system admits the solutions consisting of rarefaction waves only, it is shown that its Cauchy problem has a unique global solution which tends time-asymptotically towards the rarefaction waves, while the initial perturbation and the strength of rarefaction waves are suitably small.

关键词: rarefaction waves, reacting mixture, nonlinear stability, zero heat conductivity

Abstract: In this paper, we study the time-asymptotically nonlinear stability of rarefaction waves for the Cauchy problem of the compressible Navier-Stokes equations for a reacting mixture with zero heat conductivity in one dimension. If the corresponding Riemann problem for the compressible Euler system admits the solutions consisting of rarefaction waves only, it is shown that its Cauchy problem has a unique global solution which tends time-asymptotically towards the rarefaction waves, while the initial perturbation and the strength of rarefaction waves are suitably small.

Key words: rarefaction waves, reacting mixture, nonlinear stability, zero heat conductivity

中图分类号: 

  • 35Q30