Optimal large-time behavior of the full 3D compressible MHD system
Volume 129 / 2022
Abstract
We investigate optimal large-time behavior for higher-order spatial derivatives of strong solutions to the 3D full compressible MHD system. More precisely, we employ low-frequency and high-frequency decomposition and delicate energy estimates to show that the third-order spatial derivatives of the density, velocity and absolute temperature converge to their corresponding equilibrium states at the $L^2$-rate $(1+t)^{-\frac {3}{4}(\frac {2}{p}-1)-\frac {3}{2}}$ with $1\leq p \lt \frac {6}{5}$, which is the same as that of the heat equation, and in particular improves the $L^2$-rate $(1+t)^{-\frac {3}{4}(\frac {2}{p}-1)-\frac {1}{2}}$ in [X. K. Pu et al., Z. Agnew. Math. Phys. 64 (2013), 519–538], and the $L^2$–rate $(1+t)^{-\frac {3}{4}(\frac {2}{p}-1)-1}$ in [J. C. Gao et al., Z. Agnew. Math. Phys. 67 (2016), 23].
