Periodic solution and asymptotic stability for the magnetohydrodynamic equations with inhomogeneous boundary condition (Q2306312)

Summary: We show, using the spectral Galerkin method together with compactness arguments, the existence and uniqueness of the periodic strong solutions for the magnetohydrodynamic-type equations with inhomogeneous boundary conditions. Furthermore, we study the asymptotic stability for the time periodic solution for this system. In particular, when the magnetic field \(\mathbf{h}(x, t)\) is zero, we obtain the existence, uniqueness, and asymptotic behavior of the strong solutions to the Navier-Stokes equations with inhomogeneous boundary conditions.