Acta mathematica scientia, Series B >
GLOBAL EXISTENCE AND CONVERGENCE RATES OF SMOOTH SOLUTIONS FOR THE 3-D COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITHOUT HEAT CONDUCTIVITY
Received date: 2012-10-03
Revised date: 2013-02-28
Online published: 2014-01-20
Supported by
Supported by National Natural Science Foundation of China-NSAF (10976026) and the Research Funds for the Huaqiao Universities (12BS232).
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.
GAO Zhen-Sheng , TAN Zhong , WU Guo-Chun . GLOBAL EXISTENCE AND CONVERGENCE RATES OF SMOOTH SOLUTIONS FOR THE 3-D COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITHOUT HEAT CONDUCTIVITY[J]. Acta mathematica scientia, Series B, 2014 , 34(1) : 93 -106 . DOI: 10.1016/S0252-9602(13)60129-0
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