Global Well-Posedness for 3D Nonhomogeneous Micropolar Fluids with Density-Dependent Viscosity

We consider an initial-boundary-value problem of three-dimensional nonhomogeneous micropolar fluids with density-dependent viscosity. Based on the energy method, we establish the global existence and uniqueness of strong solutions when the initial energy is suitably small. Moreover, we show that the velocity and the micro-rotational velocity converge exponentially to zero in H-2 as time goes to infinity. In particular, there is no need to impose some compatibility condition on the initial data despite the presence of vacuum.