In this paper, by using the properties of decay character and the Fourier splitting method, we establish the time decay rates of solutions for three-dimensional incompressible electron inertial Hall-MHD equations. In particular, the optimal decay rates of the mixed space-time derivatives of the solution are obtained.
"On the well-posedness and decay characterization of solutions for incompressible electron inertial Hall-MHD equations." Adv. Differential Equations 25 (7/8) 373 - 422, July/August 2020.