Stability and large-time behavior for the 2D incompressible magneto-micropolar equations with partial mixed dissipation

This paper investigates the stability of two-dimensional (2D) incompressible anisotropic magneto-micropolar equations near hydrostatic equilibrium in a slab domain with Navier-type slip boundary condition. The system is characterized by partial mixed dissipation, including vertical dissipation, horizontal magnetic diffusion, and horizontal vortex viscosity.Based on complex anisotropic analysis, we establish the global stability of the solution. In particular, our results rigorously demonstrate that the magnetic fields enhance dissipation, thereby stabilizing the fluid dynamics. Compared to known results [H.X. Lin, S. Liu, H. Zhang, Q. Sun, Nonlinearity, 37, 2024], our approach does not impose any restrictions on the magnetic diffusion coefficient or the background magnetic field. In addition, we also provide the large-time behavior of the solution.