数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (1): 265-282.doi: 10.1016/S0252-9602(15)30094-1

• 论文 • 上一篇    下一篇

CONVERGENCE RATE OF SOLUTIONS TO STRONG CONTACT DISCONTINUITY FOR THE ONE-DIMENSIONAL COMPRESSIBLE RADIATION HYDRODYNAMICS MODEL

陈正争, 柴晓娟, 王文娟   

  1. School of Mathematical Sciences, Anhui University, Hefei 230601, China
  • 收稿日期:2014-09-15 修回日期:2015-05-25 出版日期:2016-01-30 发布日期:2016-01-30
  • 通讯作者: Zhengzheng CHEN,E-mail:chenzzandu@163.com E-mail:chenzzandu@163.com
  • 作者简介:Xiaojuan CHAI,E-mail:chaixj.ahu@gmail.com;Wenjuan WANG,E-mail:wangwenjuan@ahu.edu.cn
  • 基金资助:

    This work was supported by the Doctoral Scientific Research Funds of Anhui University(J10113190005) and the Tian Yuan Foundation of China(11426031).

CONVERGENCE RATE OF SOLUTIONS TO STRONG CONTACT DISCONTINUITY FOR THE ONE-DIMENSIONAL COMPRESSIBLE RADIATION HYDRODYNAMICS MODEL

Zhengzheng CHEN, Xiaojuan CHAI, Wenjuan WANG   

  1. School of Mathematical Sciences, Anhui University, Hefei 230601, China
  • Received:2014-09-15 Revised:2015-05-25 Online:2016-01-30 Published:2016-01-30
  • Contact: Zhengzheng CHEN,E-mail:chenzzandu@163.com E-mail:chenzzandu@163.com
  • Supported by:

    This work was supported by the Doctoral Scientific Research Funds of Anhui University(J10113190005) and the Tian Yuan Foundation of China(11426031).

摘要:

This paper is concerned with a singular limit for the one-dimensional compress-ible radiation hydrodynamics model. The singular limit we consider corresponds to the physical problem of letting the Bouguer number infinite while keeping the Boltzmann number constant. In the case when the corresponding Euler system admits a contact discontinuity wave, Wang and Xie(2011) [12] recently verified this singular limit and proved that the solution of the compressible radiation hydrodynamics model converges to the strong contact discontinuity wave in the L∞-norm away from the discontinuity line at a rate of ε1/4, as the reciprocal of the Bouguer number tends to zero. In this paper, Wang and Xie's convergence rate is improved to ε7/8 by introducing a new a priori assumption and some refined energy estimates. Moreover, it is shown that the radiation flux q tends to zero in the L∞-norm away from the discontinuity line, at a convergence rate as the reciprocal of the Bouguer number tends to zero.

关键词: radiation hydrodynamics model, singular limit, contact discontinuity, convergence rate, energy estimates

Abstract:

This paper is concerned with a singular limit for the one-dimensional compress-ible radiation hydrodynamics model. The singular limit we consider corresponds to the physical problem of letting the Bouguer number infinite while keeping the Boltzmann number constant. In the case when the corresponding Euler system admits a contact discontinuity wave, Wang and Xie(2011) [12] recently verified this singular limit and proved that the solution of the compressible radiation hydrodynamics model converges to the strong contact discontinuity wave in the L∞-norm away from the discontinuity line at a rate of ε1/4, as the reciprocal of the Bouguer number tends to zero. In this paper, Wang and Xie's convergence rate is improved to ε7/8 by introducing a new a priori assumption and some refined energy estimates. Moreover, it is shown that the radiation flux q tends to zero in the L∞-norm away from the discontinuity line, at a convergence rate as the reciprocal of the Bouguer number tends to zero.

Key words: radiation hydrodynamics model, singular limit, contact discontinuity, convergence rate, energy estimates

中图分类号: 

  • 35L65