Global existence of strong solutions to nonhomogeneous MHD system in thin three-dimensional domains

We establish the global existence of strong solutions to the nonhomogeneous incompressible magnetohydrodynamics (MHD) equations in a thin three-dimensional domain Ω = R² × (0, ϵ), with ϵ ∈ (0, 1], subject to Dirichlet boundary conditions on the top and bottom boundaries. Global well-posedness may hold for large initial data, provided the vertical thickness ϵ is sufficiently small. Moreover, when ϵ → 0⁺, both the velocity and magnetic field tend to vanish away from the initial time. The analysis is based on a priori H² estimates of the solutions, with particular attention to the dependence on the vertical parameter ϵ.