406 research outputs found
Higher-Order Global Regularity of an Inviscid Voigt-Regularization of the Three-Dimensional Inviscid Resistive Magnetohydrodynamic Equations
We prove existence, uniqueness, and higher-order global regularity of strong
solutions to a particular Voigt-regularization of the three-dimensional
inviscid resistive Magnetohydrodynamic (MHD) equations. Specifically, the
coupling of a resistive magnetic field to the Euler-Voigt model is introduced
to form an inviscid regularization of the inviscid resistive MHD system. The
results hold in both the whole space \nR^3 and in the context of periodic
boundary conditions. Weak solutions for this regularized model are also
considered, and proven to exist globally in time, but the question of
uniqueness for weak solutions is still open. Since the main purpose of this
line of research is to introduce a reliable and stable inviscid numerical
regularization of the underlying model we, in particular, show that the
solutions of the Voigt regularized system converge, as the regularization
parameter \alpha\maps0, to strong solutions of the original inviscid
resistive MHD, on the corresponding time interval of existence of the latter.
Moreover, we also establish a new criterion for blow-up of solutions to the
original MHD system inspired by this Voigt regularization. This type of
regularization, and the corresponding results, are valid for, and can also be
applied to, a wide class of hydrodynamic models
Blow-up criteria for Boussinesq system and MHD system and Landau-Lifshitz equations in a bounded domain
In this paper, we prove some blow-up criteria for the 3D Boussinesq system
with zero heat conductivity and MHD system and Landau-Lifshitz equations in a
bounded domain.Comment: 20 page
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