Abstract
In this paper, we study the time decay rates of the solution to the Cauchy problem for the compressible heat-conducting magnetohydrodynamic equations via a refined pure energy method. In particular, the optimal decay rates of the higher-order spatial derivatives of the solution are obtained. The \({\dot{H}^{-s}(0\leq s<\frac{3}{2})}\) negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates.
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Wei, R., Li, Y. & Yao, Za. Decay of the compressible magnetohydrodynamic equations. Z. Angew. Math. Phys. 66, 2499–2524 (2015). https://doi.org/10.1007/s00033-015-0536-8
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DOI: https://doi.org/10.1007/s00033-015-0536-8