In this paper, the large-time behavior of global strong solutions is justified for the three dimensional compressible micropolar fluids subjected to Hall current. Both the global existence and the optimal decay rates of strong solutions are obtained when the smooth initial data are sufficiently close to the non-vacuum equilibrium in $H^1$. In addition, the vanishing limit of the Hall coefficient is also justified.

In this paper, we considered the global well-posedness of strong solutions to the Cauchy problem of three-dimensional (3D) nonhomogeneous incompressible micropolar fluids with density-dependent viscosity and vacuum. Based on the energy method, some key a priori exponential decay-in-time rates of strong solutions are obtained. As a result, the existence and large-time asymptotic behavior of strong solutions in the whole space ${\mathbb{R}}^3$ are established, provided that the initial mass is sufficiently small. Note that this result is proven without any compatibility conditions.

This article established the global existence and uniqueness of solutions for the 3D compressible magneto-micropolar fluid system with vacuum. The remarkable thing is that in the context of small initial energy, we got a new result with a lower regularity than we ever have before.