Global existence for two regularized MHD models in three space-dimension

Abstract

The global existence of solutions for the 3D incompressible Euler equations is a major open problem. For the 3D inviscid MHD system, the global existence is an open problem as well. Our main concern in this paper is to understand which kind of regularization, of the form of $\alpha$-regularization or partial viscous regularization, is capable to provide the global in time solvability for the 3D inviscid MHD system of equations. We consider two different regularized magnetohydrodynamic models for an incompressible fluid. In both cases, we provide a global existence result for the solution of the system.