Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An example elucidating the mathematical situation in the statistical
  non-uniqueness problem of turbulence   An instructive example is presented to elucidate the mathematical situation
in the non-uniqueness problem of the infinite Friedmann-Keller hierarchy of
equations for all multi-point moments within the theory of spatially unbounded
Navier-Stokes turbulence. It is shown that the non-uniqueness problem of the
Friedmann-Keller hierarchy emerges from the property that the system of
equations is defined forward recursively. As a result, this system does not
possess a unique general solution, even when the complete infinite system is
formally considered. That is, even when imposing a sufficient number of initial
conditions to this infinite system, it still does not provide a unique
solution. This finding is supported by a Lie-group invariance analysis, in that
the imposed example analogous to the Friedmann-Keller hierarchy admits an
unclosed Lie algebra which allows for infinitely many functionally different
equivalence transformations which all can be made compatible with any
specifically chosen initial condition. Hence, if no prior modelling assumptions
are made to close the Friedmann-Keller system of equations, the existence of an
invariant solution within such a forward recursively defined system is then
without value, since it just represents an arbitrary solution among infinitely
many other, equally privileged invariant solutions.

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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys