Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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
$\varepsilon$-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.

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The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org