Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The 2D Incompressible Magnetohydrodynamics Equations with only Magnetic
  Diffusion   This paper examines the global (in time) regularity of classical solutions to
the 2D incompressible magnetohydrodynamics (MHD) equations with only magnetic
diffusion. Here the magnetic diffusion is given by the fractional Laplacian
operator $(-\Delta)^\beta$. We establish the global regularity for the case
when $\beta>1$. This result significantly improves previous work which requires
$\beta>\frac32$ and brings us closer to the resolution of the well-known global
regularity problem on the 2D MHD equations with standard Laplacian magnetic
diffusion, namely the case when $\beta=1$.

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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
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The categories of this paper are: stat
31
The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio