Remarks on the regularity criteria of three-dimensional magnetohydrodynamics system in terms of two velocity field components

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 two velocity vector field components eliminating the condition on the third component completely. The proof consists of a new decomposition of the four nonlinear terms of the system and estimating a component of the magnetic vector field in terms of the same component of the velocity vector field. This result may be seen as a component reduction result of many previous works [C. He and Z. Xin, " On the regularity of weak solutions to the magnetohydrodynamic equations, " J.