数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (1): 93-106.doi: 10.1016/S0252-9602(13)60129-0

• 论文 • 上一篇    下一篇

GLOBAL EXISTENCE AND CONVERGENCE RATES OF SMOOTH SOLUTIONS FOR THE 3-D COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITHOUT HEAT CONDUCTIVITY

高真圣*|谭忠|吴国春   

  1. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China; School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
  • 收稿日期:2012-10-03 修回日期:2013-02-28 出版日期:2014-01-20 发布日期:2014-01-20
  • 通讯作者: 高真圣,gaozhensheng@hqu.edu.cn E-mail:gaozhensheng@hqu.edu.cn;ztan85@163.com; guochunwu@126.com
  • 基金资助:

    Supported by National Natural Science Foundation of China-NSAF (10976026) and the Research Funds for the Huaqiao Universities (12BS232).

GLOBAL EXISTENCE AND CONVERGENCE RATES OF SMOOTH SOLUTIONS FOR THE 3-D COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITHOUT HEAT CONDUCTIVITY

 GAO Zhen-Sheng*, TAN Zhong, WU Guo-Chun   

  1. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China; School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
  • Received:2012-10-03 Revised:2013-02-28 Online:2014-01-20 Published:2014-01-20
  • Contact: GAO Zhen-Sheng,gaozhensheng@hqu.edu.cn E-mail:gaozhensheng@hqu.edu.cn;ztan85@163.com; guochunwu@126.com
  • Supported by:

    Supported by National Natural Science Foundation of China-NSAF (10976026) and the Research Funds for the Huaqiao Universities (12BS232).

摘要:

In this paper, we are concerned with the global existence and convergence rates of the smooth solutions for the compressible magnetohydrodynamic equations without heat conductivity, which is a hyperbolic-parabolic system. The global solutions are obtained by combining the local existence and a priori estimates if H3-norm of the initial perturbation around a constant states is small enough and its L1-norm is bounded. A priori decay-in-time estimates on the pressure, velocity and magnetic field are used to get the uniform bound of entropy. Moreover, the optimal convergence rates are also obtained.

关键词: magnetohydrodynamics, optimal convergence rate, decay-in-time estimates

Abstract:

In this paper, we are concerned with the global existence and convergence rates of the smooth solutions for the compressible magnetohydrodynamic equations without heat conductivity, which is a hyperbolic-parabolic system. The global solutions are obtained by combining the local existence and a priori estimates if H3-norm of the initial perturbation around a constant states is small enough and its L1-norm is bounded. A priori decay-in-time estimates on the pressure, velocity and magnetic field are used to get the uniform bound of entropy. Moreover, the optimal convergence rates are also obtained.

Key words: magnetohydrodynamics, optimal convergence rate, decay-in-time estimates

中图分类号: 

  • 35Q35