Global weighted regularity for the 3D axisymmetric non-resistive MHD system

Abstract

We consider the regularity criteria of axisymmetric solutions to the non-resistive MHD system with non-zero swirl in $ \mathbb{R}^{3} $. By applying a new anisotropic Hardy-Sobolev inequality in mixed Lorentz spaces, we show that strong solutions to this system can be smoothly extended beyond the possible blow-up time $ T $ if the horizontal angular component of the velocity belongs to anisotropic Lorentz spaces.

Keywords

• non-resistive mhd system
• anisotropic lorentz spaces
• regularity criteria