# American Institute of Mathematical Sciences

September  2010, 14(2): 603-627. doi: 10.3934/dcdsb.2010.14.603

## On the higher-order global regularity of the inviscid Voigt-regularization of three-dimensional hydrodynamic models

 1 Department of Mathematics, University of California, Irvine, Irvine CA 92697-3875, United States 2 Department of Mathematics and Department of Mechanics and Aerospace Engineering, University of California, Irvine, CA 92697, United States

Received  September 2009 Revised  February 2010 Published  June 2010

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.
Citation: Adam Larios, E. S. Titi. On the higher-order global regularity of the inviscid Voigt-regularization of three-dimensional hydrodynamic models. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 603-627. doi: 10.3934/dcdsb.2010.14.603
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