Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact Solutions on Twisted Rings for the 3D Navier-Stokes Equations   The problem of describing the behavior of the solutions to the Navier-Stokes
equations in three space dimensions has always been borderline. From one side,
due to the viscosity term, smooth data seem to produce solutions with an
everlasting regular behavior. On the other hand, the lack of a convincing
theoretical analysis suggests the existence of possible counterexamples. In
particular, one cannot exclude the blowing up of solutions in finite time even
in presence of smooth data. Here we give examples of explicit solutions of the
non-homogeneous equations. These are defined on a Hill's type vortex where the
flow is rotating and swirling at the same time, inducing the flux to spiraling
at a central node. Despite the appearance, the solution still remains very
regular at the agglomeration point. The analysis may lead to a better
understanding of the subtle problem of characterizing the solution space of the
3D Navier-Stokes equations. For instance, this result makes more narrow the
path to the search of counterexamples built on the stretching and twisting of
vortex tubes.

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The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: math
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The categories of this paper are: q-alg