Periodic Solution and Asymptotic Stability for the Magnetohydrodynamic Equations with Inhomogeneous Boundary Condition - Igor Kondrashuk; Eduardo Alfonso Notte-Cuello; Mariano Poblete-Cantellano; Marko Antonio Rojas-Medar (Axioms, 2019)
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 <semantics> h ( x , t ) </semantics> is zero, we obtain the existence, uniqueness, and asymptotic behavior of the strong solutions to the Navier–Stokes equations with inhomogeneous boundary conditions.