ABSTRACT In this paper, we investigate the stability of perturbations near the hydrostatic equilibrium of the two‐dimensional incompressible Boussinesq‐MHD equations with zero resistivity. The absence of vertical dissipation of the magnetic field poses significant challenges to stability analysis. The main technique is utilizing anisotropic estimates and the vertical spatial decomposition, and then we can establish the global stability of a certain stationary in two kinds of infinite strip domain: and .
Hao Liu (Tue,) studied this question.