Global Attractor and Singular Limits of the 3D Voigt-regularized Magnetohydrodynamic Equations

In this article, the 3D Voigt-regularized Magnetohydrodynamic equations are considered, for which it is unknown if the uniqueness of weak solution exists. First, we prove that the uniform global attractor exists by constructing an evolutionary system. Then singular limits of this system are established. Namely, when a certain regularization parameter disappears, the convergence of global attractors is shown between the 3D autonomous Voigt-regularized Magnetohydrodynamic equations and Magnetohydrodynamic equations.