Global classical solutions for 3D compressible magneto-micropolar fluids without resistivity and spin viscosity in a strip domain

In this paper, we consider 3D compressible magneto-micropolar fluids without resistivity and spin viscosity in a strip domain. The prominent character of the governing model is the presence of the microstructure, a linear coupling structure involving derivatives of the velocity fields, which along with the lack of spin viscosity brings several challenges to the analysis. By exploiting the two-tier energy method developed in Guo and Tice (Arch Ration Mech Anal, 2013), we prove the global existence of classical solutions to the governing model around a uniform magnetic field that is non-parallel to the horizontal boundary. Moreover, we show that the solution converges to the steady state at an almost exponential rate as time goes to infinity. One of the main ingredients in our analysis, compared with previous works on micropolar fluids, is that we deal with the microstructure by establishing some delicate estimates based on the analysis of the div-curl decomposition, and the coupling between the fluid velocity and the vorticity of angular velocity.