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) uθ=0,Br=Bz=0, (2) Br=Bz=0, and (3) Bθ=0. 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 ωθ and the angular current density field jθ. Copyright © 2016 John Wiley & Sons, Ltd.
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