On the regularity of weak solutions to the magnetohydrodynamic equations

Abstract

In this paper, we study the regularity of weak solution to the incompressible magnetohydrodynamic equations. We obtain some sufficient conditions for regularity of weak solutions to the magnetohydrodynamic equations, which is similar to that of incompressible Navier–Stokes equations. Moreover, our results demonstrate that the velocity field of the fluid plays a more dominant role than the magnetic field does on the regularity of solution to the magneto-hydrodynamic equations.