Decay of the compressible magnetohydrodynamic equations

Abstract

In this paper, we study the time decay rates of the solution to the Cauchy problem for the compressible heatconducting 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. TheḢ −s (0 ≤ s < 3 2 ) negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates.Mathematics Subject Classification. 35Q30 · 76N15 · 76P05 · 82C40.

Liouville type Theorems for the stationary compressible 3D MHD equations

“…Comparing to the steady incompressible MHD equations, we refer to [32] and [34]. The long-time behavior of a small global solution can be found in [9], [31].…”