On the Higher-Order Global Regularity of the Inviscid\n Voigt-Regularization of Three-Dimensional Hydrodynamic Models

We prove higher-order and a Gevrey class (spatial analytic) regularity of\nsolutions to the Euler-Voigt inviscid $\\alpha$-regularization of the\nthree-dimensional Euler equations of ideal incompressible fluids. Moreover, we\nestablish the convergence of strong solutions of the Euler-Voigt model to the\ncorresponding solution of the three-dimensional Euler equations for inviscid\nflow on the interval of existence of the latter. Furthermore, we derive a\ncriterion for finite-time blow-up of the Euler equations based on this inviscid\nregularization. The coupling of a magnetic field to the Euler-Voigt model is\nintroduced to form an inviscid regularization of the inviscid irresistive\nmagneto-hydrodynamic (MHD) system. Global regularity of the regularized MHD\nsystem is also established.\n