ON THE HIGHER-ORDER GLOBAL REGULARITY OF THE INVISCID VOIGT-REGULARIZATION OF THREE-DIMENSIONAL HYDRODYNAMIC MODELS uri icon

abstract

  • We prove higher-order and a Gevrey class (spatial analytic) regularity of solutions to the Euler-Voigt inviscid -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.

published proceedings

  • DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B

author list (cited authors)

  • Larios, A., & Titi, E. S.

citation count

  • 52

complete list of authors

  • Larios, Adam||Titi, Edriss S

publication date

  • September 2010