Regularity of weak solutions to the magneto-hydrodynamics equations in terms of the direction of velocity

Abstract

In this article, we study the regularity of weak solutions to the 3D incompressible magneto-hydrodynamics equations. We obtain a new class of regularity criteria in terms of the direction of the velocity. Our result extend some results known for incompressible Navier-Stokes equations.

Keywords

• Magneto-hydrodynamics equation
• regularity
• Serrin criteria