Stability of vertically charged steady magnetic field in 3D incompressible magneto-micropolar fluids without magnetic and angular viscosity in a strip domain

Abstract

This paper intends to understand the regularity and stability problem on the 3D incompressible magneto-micropolar equations with zero magnetic and angular viscosities in a strip domain. The magneto-micropolar system models the electrically conducting micropolar fluid in the presence of a magnetic field. The lack of magnetic diffusion and angular dissipation makes it impossible to prove even small data global well-posedness result, let alone general large data global regularity. This paper presents a steady-state setup around which any perturbations can be shown to be globally regular and stable. More precisely, any small perturbation near a steady magnetic field perpendicular to the horizontal boundary leads to a unique global classical solution. In addition, the solution is shown to converge to the steady state at an almost exponential rate as time goes to infinity. These appear to be the very first rigorous global results on the magneto-micropolar equations concerned here.