Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence, regularity and uniqueness of weak solutions with bounded
  magnetic fields to the steady Hall-MHD system   Under the condition of small external forces, we obtain existence of a weak
solution of the steady Hall-MHD system with H\"{o}lder continuous magnetic
field. We also established regularity of weak solutions provided that magnetic
fields are bounded. For sufficiently small external forces, uniqueness result
is also established.

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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: econ
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys