On regularity criteria for MHD system in anisotropic Lebesgue spaces

Abstract

This paper concerns the regularity criteria of the three-dimensional magnetohydrodynamic (MHD) system in anisotropic Lebesgue spaces. Two regularity results were proved under additional assumptions on the horizontal components of the velocity field $ {{\bf{u}}} $ and the magnetic field $ {{\bf{B}}} $, or directions of Elsässer's variables $ {{\bf{u}}}\pm{{\bf{B}}} $.

Keywords

• mhd system
• regularity criteria
• anisotropic lebesgue space
• sum spaces
• elsässer's variables