Global existence and optimal convergence rates of solutions for 3D compressible magneto-micropolar fluid equations

The Cauchy problem for the three-dimensional compressible magneto-micropolar fluid equations is considered. Existence of global-in-time smooth solutions is established under the condition that the initial data are small perturbations of some given constant state. Moreover, we obtain the time decay rates of the higher-order spatial derivatives of the solution by combining the Lp-Lq estimates for the linearized equations and the Fourier splitting method, if the initial perturbation is small in H3-norm and bounded in L1-norm.