Articles you may be interested in Remarks on the regularity criteria of generalized MHD and Navier-Stokes systems Regularity criteria of weak solutions to the three-dimensional micropolar flows Remarks on the blow-up criteria for three-dimensional ideal magnetohydrodynamics equations We study the three-dimensional magnetohydrodynamics system and obtain its regularity criteria in terms of only t...

We apply the finite element method to two-dimensional, incompressible MHD, using a streamfunction approach to enforce the divergence-free conditions on the magnetic and velocity fields. This problem was considered by Strauss and Longcope [SL98]. In this paper, we solve the problems with magnetic and velocity fields instead of the velocity stream function, magnetic flux, and their derivatives. C...