On analyticity and temporal decay rates of solutions to the viscous resistive Hall-MHD system

We address the analyticity and large time decay rates for strong solutions of the Hall-MHD equations. By Gevrey estimates, we show that the strong solution with small initial date in $H^r({\mathbb{R}}^3)$ with $r>\text{f}52$ becomes analytic immediately after $t>0$, and the radius of analyticity will grow like $\sqrt{t}$ in time. Upper and lower bounds on the decay of higher order derivatives are also obtained, which extends the previous work by Chae and Schonbek (J. Differential Equations 255 (2013), 3971–3982).