A regularity criterion of 3D incompressible MHD system with mixed pressure-velocity-magnetic field

Abstract

This work focuses on the 3D incompressible magnetohydrodynamic (MHD) equations with mixed pressure-velocity-magnetic field in view of Lorentz spaces. Our main result shows the weak solution is regular, provided that π e−|x| 2 + |u| + |b| θ ∈ L p (0, T; L q,∞), where 2 p + 3 q = 2 − θ and 0 ≤ θ ≤ 1.

Keywords

• mhd equations
• regularity criterion
• a priori estimates