Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homogeneous solutions of stationary Navier-Stokes equations with
  isolated singularities on the unit sphere. I. One singularity   We classify all $(-1)-$homogeneous axisymmetric no swirl solutions of
incompressible stationary Navier-Stokes equations in three dimension which are
smooth on the unit sphere minus the south pole, parameterize them as a two
dimensional surface with boundary, and analyze their pressure profiles near the
north pole. Then we prove that there is a curve of $(-1)-$homogeneous
axisymmetric solutions with nonzero swirl, having the same smoothness property,
emanating from every point of the interior and one part of the boundary of the
solution surface. Moreover we prove that there is no such curve of solutions
for any point on the other part of the boundary. We also establish asymptotic
expansions for every (-1)-homogeneous axisymmetric solutions in a neighborhood
of the singular point on the unit sphere.

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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: stat
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an