Uniform regularity and vanishing dissipation limit for the incompressible magneto-micropolar fluid equations with transverse magnetic field

This paper explores the influence of a transverse magnetic field at the boundary and studies the vanishing dissipation limit of the incompressible magneto-micropolar fluid equations in a half-space. We prove that the solutions remain uniformly bounded, both in the conormal Sobolev norms and the $L^{\mathrm{\infty }}$ norm, over a fixed time interval, independent of the dissipative coefficients. As a result, we establish the convergence of the dissipative magneto-micropolar fluid equations to the corresponding non-dissipative equations in the $L^{\mathrm{\infty }}$ norm. Additionally, our analysis provides uniform regularity energy estimates as the dissipative coefficients tend to zero. This shows that the strong boundary layer can still be prevented by the transverse magnetic field, even with the magnetic diffusion.