Consider the time decay rates of the smooth solution to the compressible MHD system on ${\mathbb{T}}^3$. It is shown that if the density ρ is uniformly bounded from up and below, and the $L^6$ norm of the magnetic H is uniformly bounded, then all derivatives of the smooth solution to the compressible MHD system decay exponentially fast to the equilibrium. Furthermore, we construct a global smooth solution obeying these decay rates with small energy but possibly large oscillations.

中文翻译：

---

可压缩磁流体动力方程光滑解的衰减估计。 ${\mathbb{Ť}}^3$

考虑可压缩MHD系统的光滑解的时间衰减率 ${\mathbb{Ť}}^3$。结果表明，如果密度ρ从上到下均匀地有界，则${\mathrm{大号}}^6$磁H的范数是均匀有界的，那么光滑方程组到可压缩MHD系统的所有导数都会快速衰减到平衡。此外，我们构造了一个全局平滑解，以较小的能量但可能较大的振动服从这些衰减率。