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 = R 2 × ( 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 H 2 estimates of the solutions, with particular attention to the dependence on the vertical parameter ϵ .