Global well-posedness and decay estimates to the 3D Cauchy problem of nonhomogeneous magneto-micropolar fluid equations with vacuum

Abstract

We investigate a model of nonhomogeneous magneto-micropolar fluids in the whole three-dimensional space R3. Under the assumption that the initial energy is suitably small, we prove the global existence and decay estimates of strong solutions. Moreover, there is no need to impose some compatibility condition on the initial data via time weighted techniques although the system under consideration degenerates near vacuum. Our analysis is based on delicate energy estimates and the structural characteristics of the model.