GLOBAL EXISTENCE AND CONVERGENCE RATES OF SMOOTH SOLUTIONS FOR THE 3-D COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITHOUT HEAT CONDUCTIVITY |
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Authors: | Zhensheng GAO School of Mathematical Sciences Huaqiao University Quanzhou China Zhong TAN Guochun WU |
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Institution: | [1]School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China [2]School of Mathematical Sciences, Xiamen University, Xiamen 361005, China |
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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-intime 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. |
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Keywords: | magnetohydrodynamics optimal convergence rate decay-in-time estimates |
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