Regularity criteria for the three-dimensional axially symmetric non-resistive incompressible magnetohydrodynamic system

In this paper, we study the three-dimensional axially symmetric non-resistive incompressible magnetohydrodynamic system. By establishing a rough blow-up criteria on ωθr, we show a Ladyzhenskaya–Prodi–Serrin type regularity criteria with respect to the swirl component uθ of the velocity.