Abstract. 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 k 3) order spatial derivative for the global solution converging to the constant state at the optimal time decay rates in L² as (1+t) ^- (3{4+k2) } with H³ 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) ^- (3{4+k2) }. Therefore, these time decay rates are shown to be optimal.
He et al. (Thu,) studied this question.