Partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equations

Abstract

This paper establishes a regularity theory for the magnetohydrodynamics (MHD) equations with external forces through scaling analysis. Inspired by the existing methodology, we utilize linearized approximations and the monotonicity property of harmonic functions to construct iterative sequences capturing scaling properties. This work successfully extends Navier-Stokes techniques to MHD coupling and demonstrates that the one dimensional parabolic Hausdorff measure of the possible singular points for the suitable weak solutions is zero.