Optimal time decay rates of the full compressible Hall-magnetohydrodynamics equations*

<bold>Abstract.</bold> In this paper, we study the time decay rates of strong solutions to the three dimensional full compressible Hall-magnetohydrodynamics equations. Firstly, we establish the upper bounds of the $k(0 \le k \le 3)$ order spatial derivative for the global solution converging to the constant state at the optimal time decay rates in $L^2$ as $(1+t)^{-(\frac{3}{4}+\frac{k}{2})}$ with $H^3$ initial data, which improves the critical spatial derivative for the density, velocity and the temperature in [S. Lai, X. Xu, and J. Zhang, Z. Angew. Math. Phys., 70 (5):139, 2019)[cite: 22331, 22332]. Then, under suitable additional low frequency assumptions on initial data, the lower bounds of the time decay rates for the global solution are also given as $(1+t)^{-(\frac{3}{4}+\frac{k}{2})}$. Therefore, these time decay rates are shown to be optimal.