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

Periodic solution and asymptotic stability for the magnetohydrodynamic equations with inhomogeneous boundary condition