On magnetic inhibition theory in 3D inhomogeneous incompressible magneto-micropolar fluids with large density

This paper is concerned with the three-dimensional inhomogeneous incompressible magneto-micropolar fluid equations on the periodic domain with dissipation acting only in the velocity equation. Unlike previous works, no magnetic or angular dissipation is assumed, while the initial density is allowed to exhibit arbitrarily large variations. We construct the global well-posedness and time decay rates of smooth solutions in high-order Sobolev spaces, provided the initial velocity, micro-rotational velocity, and magnetic field are small perturbations of equilibrium. Our analysis reveals how a background magnetic field satisfying a Diophantine condition generates a stabilizing mechanism that prevents singularity formation, despite the absence of magnetic and angular dissipation.