Global Existence and Optimal Decay Rates of Solutions for Three‐Dimensional Compressible Magneto‐Micropolar Fluids With External Force

ABSTRACT In this paper, we studied the Cauchy problem of three‐dimensional compressible magneto‐micropolar fluids with a potential external force. Based on the smallness assumption on both the initial perturbation and the external force in some Sobolev space, the existence of global‐in‐time smooth solutions is established. Moreover, we established the optimal convergence rates of the higher‐order spatial derivatives of the solution by combining the estimates for the linearized equations and the Fourier splitting method, if the initial perturbation is small in ‐norm and bounded in ‐norm.