On the Cauchy problem of 3D nonhomogeneous micropolar fluids with density-dependent viscosity

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 densitydependent viscosity and vacuum. Based on the energy method, some key a priori exponential decayin-time rates of strong solutions are obtained. As a result, the existence and large-time asymptotic behavior of strong solutions in the whole space R3 are established, provided that the initial mass is sufficiently small. Note that this result is proven without any compatibility conditions.