Regularity criteria for suitable weak solutions to the four dimensional incompressible magneto-hydrodynamic equations near boundary

In this paper, we consider suitable weak solutions of the four dimensional incompressible magneto-hydrodynamic equations. We give two different kind ε  -regularity criteria. One only requires the smallness of scaling Lp,qLp,q norm of u  , another requires the smallness of scaling space time L2L2 norm of ∇u and boundedness of scaling norm of H or ∇H. And as an application of the second kind criteria, we also prove that up to the boundary, the two-dimensional Hausdorff measure of the set of singular points is equal to zero.