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

摘要

In this paper, we consider suitable weak solutions of the four dimensional incompressible magneto-hydrodynamic equations. We give two different kind epsilon-regularity criteria. One only requires the smallness of scaling L-p,L-q norm of u, another requires the smallness of scaling space time L-2 norm of del u and boundedness of scaling norm of H or del 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. (C) 2015 Elsevier Inc. All rights reserved.