Global well‐posedness of the 3D hydrostatic magnetohydrodynamics equations

In this paper, the three‐dimensional hydrostatic magnetohydrodynamic (HMHD) equations are considered on a thin domain. We showed the global existence and uniqueness (regularity) of strong solutions to the three‐dimensional incompressible HMHD equations without any small assumption on the initial data. More precisely, there exists a unique strong solution globally in time for any given ‐smooth initial data.