On the higher-order global regularity of the inviscid Voigt-regularization of three-dimensional hydrodynamic models Academic Article uri icon

abstract

  • 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.

citation count

  • 43

publication date

  • January 2010