  We show, using the spectral Galerkin method together with compactness
arguments, existence and uniqueness of the periodic strong solutions for the
magnetohydrodynamics's type equations with inhomogeneous boundary conditions.
Also, we study the asymptotic stability for time periodic solution for this
system. In particular, when the magnetic field h(x,t) is zero, we obtain
existence, uniqueness and asymptotic behavior of the strong solutions to the
Navier-Stokes equations with inhomogeneous boundary conditions.
