Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and uniqueness of low-energy weak solutions to the
  compressible 3D magnetohydrodynamics equations   We prove the existence and uniqueness of weak solutions of the three
dimensional compressible magnetohydrodynamics (MHD) equations. We first obtain
the existence of weak solutions with small $L^2$-norm which may display
codimension-one discontinuities in density, pressure, magnetic field and
velocity gradient. The weak solutions we consider here exhibit just enough
regularity and structure which allow us to develop uniqueness and continuous
dependence theory for the compressible MHD equations. Our results generalise
and extend those for the intermediate weak solutions of compressible
Navier-Stokes equations.

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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci