Regularity Criteria for the 3D Magneto-Hydrodynamics Equations in Anisotropic Lorentz Spaces

In this paper, we investigate the regularity of weak solutions to the 3D incompressible MHD equations. We provide a regularity criterion for weak solutions involving any two groups functions (partial derivative(1)u(1), partial derivative(1)b(1)), (partial derivative(2)u(2), partial derivative(2)b(2)) and (partial derivative(3)u(3), partial derivative(3)b(3)) in anisotropic Lorentz space.

Automated summary

This paper investigates the regularity of weak solutions to the 3D incompressible MHD equations, providing a regularity criterion for weak solutions involving any two groups of functions in anisotropic Lorentz space.