One component regularity criteria for the axially symmetric MHD-Boussinesq system

<p style='text-indent:20px;'>In this paper, we consider regularity criteria of a class of 3D axially symmetric MHD-Boussinesq systems without magnetic resistivity or thermal diffusivity. Under some Prodi-Serrin type critical assumptions on the horizontal angular component of the velocity, we will prove that strong solutions of the axially symmetric MHD-Boussinesq system can be smoothly extended beyond the possible blow-up time <inline-formula><tex-math id="M1">\begin{document}$ T_\ast $\end{document}</tex-math></inline-formula> if the magnetic field contains only the horizontal swirl component. No a priori assumption on the magnetic field or the temperature fluctuation is imposed.</p>