Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Blow up of smooth solutions to the barotropic compressible
  magnetohydrodynamic equations with finite mass and energy   We prove that the smooth solutions to the Cauchy problem for the
three-dimensional compressible barotropic magnetohydrodynamic equations with
conserved total mass and finite total energy lose the initial smoothness within
a finite time. Further, we show that the same result holds for the solution to
the Cauchy problem for the multidimensional compressible Navier-Stokes system.
Moreover, for the solution with a finite momentum of inertia we get the
two-sided estimates of different components of total energy.

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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: physics