On the higher-order global regularity of the inviscid Voigt-regularization of three-dimensional hydrodynamic models
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We prove higher-order and a Gevrey class (spatial analytic) regularity of solutions to the Euler-Voigt inviscid α-regularization of the threedimensional 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 magnetohydrodynamic (MHD) system. Global regularity of the regularized MHD system is also established.
author list (cited authors)
Larios, A., & S. Titi, E.