We show existence and uniqueness of strong periodic solutions to the magnetohydrodynamic (MHD) equations in an arbitrary 3D bounded domain Ω with smooth boundary ∂Ω. It should be emphasized that we do not need to impose any geometric condition on Ω. Based on the L r -theorem of the magnetic Laplace operator by 14 , we develop the method of 11 for construction of global mild solutions with small periodic external forces. We also prove that our solution becomes necessarily regular provided the given data are certainly smooth.
Kozono et al. (Fri,) studied this question.