Global regularity criteria of the 3D MHD-Boussinesq equations without thermal diffusion

We study the global regularity for the three dimensional incompressible magnetohydrodynamic-Boussinesq (MHD-Boussinesq) equations. By establishing some sufficient regularity conditions in terms of partial components of velocity and magnetic fields, we prove that solutions to the MHD-Boussinesq equations without thermal diffusivity will not blow-up in any finite time.