Global well-posedness to the 3D Cauchy problem of nonhomogeneous micropolar fluids involving density-dependent viscosity with large initial velocity and micro-rotational velocity

We show the global well-posedness to the three-dimensional (3D) Cauchy problem of nonhomogeneous micropolar fluids with density-dependent viscosity and vacuum in R 3 provided that the initial mass is sufficiently small.Moreover, we also obtain that the gradients of velocity and micro-rotational velocity converge exponentially to zero in H 1 as time goes to infinity.Our analysis relies heavily on delicate energy estimates and the structural characteristic of the system under consideration.In particular, the initial velocity and micro-rotational velocity could be arbitrarily large.