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

Abstract

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 $L^{p,q}$ norm of $u$, another requires the smallness of scaling space time $L^2$ norm of $\nabla u$ and boundedness of scaling norm of $H$ or $\nabla H$. 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.

arXiv admin note: substantial text overlap with arXiv:1309.3348, arXiv:1302.1443; and text overlap with arXiv:1101.5580 by other authors

References in corpus (3)

• On the regularity criterion of weak solution for the 3D viscous Magneto-hydrodynamics equations
• The Beale-Kato-Majda criterion to the 3D Magneto-hydrodynamics equations
• Boundary regularity criteria for suitable weak solutions of the magnetohydrodynamic equations