Abstract:

This paper focus on time decay rate for large-solution about compressible magnetohydrodynamic equations in $\mathbb{R}^3$. Provided that $(\sigma_{0}-1,u_{0},M_{0})\in L^1\cap H^2$, based on the work of Chen et al.[1], $\|\nabla(\sigma-1,u,M)\|_{H^1}\leqslant C(1+t)^{-\frac{5}{4}}$ is obtained in reference [2], obviously, time decay rate of the 2nd-order derivative of the solution in [2] is not ideal. Here, we improve that of $\|\nabla^2 (\sigma-1,u,M)\|_{L^2}$ to be $(1+t)^{-\frac{7}{4}}$ by the frequency decomposition method[3].

Key words: Time decay rate, Large-solution, Compressible magnetohydrodynamic equations