One component regularity criteria for the axially symmetric MHD-Boussinesq system: criteria on the swirl component of the velocity

Abstract

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 $T_{\ast }$ if the magnetic field contains only the horizontal swirl component. No a priori assumption on the magnetic field and the temperature fluctuation is imposed.

arXiv comment20 pages, all comments are welcome

References in corpus (4)

• On the regularity criterion of weak solution for the 3D viscous Magneto-hydrodynamics equations
• On the global well-posedness for the Boussinesq system with horizontal dissipation
• Global well-posedness for the Navier-Stokes-Boussinesq system with axisymmetric data
• Global regularity of solutions for the 3D non-resistive and non-diffusive MHD-Boussinesq system with axisymmetric data

Cited by in corpus (2)

• Global regularity of solutions for the 3D non-resistive and non-diffusive MHD-Boussinesq system with axisymmetric data
• A refined long time asymptotic bound for 3D axially symmetric Boussinesq system with zero thermal diffusivity