Global well-posedness and exponential stability of 3D incompressible magneto-micropolar fluids with density-dependent viscosities and resistivity

This paper studies the global existence and large-time behavior of strong solutions to an initial-boundary value problem of the three-dimensional (3D) nonhomogeneous incompressible magneto-micropolar fluids with density-dependent viscosities and resistivity in the presence of vacuum states. Based on some key a priori exponential decay-in-times rates of the strong solutions, we get the existence, uniqueness and exponential stability of the global strong solutions in an bounded domain, provided that the initial energy is suitably small. Note that, there is no need to impose any smallness conditions on the initial density despite the presence of vacuum. This is the first result of the 3D magneto-micropolar fluids with all viscosities and resistivity depending density in a bounded domain. We also give the detailed proof of uniqueness.