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

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+k/2) 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+k/2). Therefore, these time decay rates are shown to be optimal.