On the regularity of the axially symmetric solutions to the three‐dimensional MHD equations

Abstract

We present the improved three-dimensional axially symmetric incompressible magnetohydrodynamics (MHD) equations with nonzero swirl. We consider three kinds of smooth axially symmetric particular solutions to the MHD equations: (1)In particular, we derive new regularity criteria for these three kinds of the three-dimensional axially symmetric smooth solutions to the MHD equations. Our results also reveal some interesting dynamic behavior of the interaction by the angular vorticity field !  and the angular current density field j  .