On a Voigt-regularization of three-dimensional magnetohydrodynamic equations

We consider a Voigt-regularization of three-dimensional magnetohydrodynamic (MHD) equations in bounded domains with periodic boundary conditions. Under suitable assumptions on the external forces, we first prove the existence, uniqueness and Sobolev regularity of solutions to the equations. Then we investigate the convergence of solutions of the Voigt-regularization to that of the classical MHD equations as the regularization parameter tends to 0. We also estimate the number of determining nodes for the solutions of the equations. Finally, when the external forces are time-independent, we show the existence of a finite-dimensional global attractor for the associated continuous semigroup.