  We prove higher-order and a Gevrey class (spatial analytic) regularity of
solutions to the Euler-Voigt inviscid $\alpha$-regularization of the
three-dimensional Euler equations of ideal incompressible fluids. Moreover, we
establish the convergence of strong solutions of the Euler-Voigt model to the
corresponding solution of the three-dimensional Euler equations for inviscid
flow on the interval of existence of the latter. Furthermore, we derive a
criterion for finite-time blow-up of the Euler equations based on this inviscid
regularization. The coupling of a magnetic field to the Euler-Voigt model is
introduced to form an inviscid regularization of the inviscid irresistive
magneto-hydrodynamic (MHD) system. Global regularity of the regularized MHD
system is also established.
