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

2014/05/19 by Gu, Xumin
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1405.4616

Abstract

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 L^p,q norm of u, another requires the smallness of scaling space time L² 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.

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