Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Condition On Spherical Surfaces To Non-Existence Of Incompressible
  Velocity Fields   In an incompressible velocity field, the surface area of a volume varies with
time, but volume remains unchanged. If incidentally the surface becomes
spherical along time, the area reaches a local minimum, since sphere has the
least area that surrounds a volume. So the area is a function of time that is
locally convex at this point. When applied to an incompressible Navier--Stokes
fluid, this property is used to work out an inequality that suggest a criterion
to non-existence of initial configurations of velocity fields, revealing its
impossibility to evolve with time. Three velocity fields are proposed as
examples. One of them agrees the inequality, the other two violate it.

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The categories of this paper are: atom-ph
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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: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an