Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the behavior of homogeneous, isotropic and stationary turbulence   The recent development of a statistical model for incompressible
Navier-Stokes (NS) fluids based on inverse kinetic theory (IKT, 2004-2008)
poses the problem of searching for particular realizations of the theory which
may be relevant for \textit{the statistical description of turbulence} and in
particular for the so-called \textit{homogeneous, isotropic}and
\textit{stationary} turbulence (HIST). Here the problem is set in terms of the
$1-$point velocity probability density function (PDF) which determines a
complete IKT-statistical model for NS fluids. This raises the interesting
question of identifying the statistical assumptions under which a Gaussian PDF
can be achieved in such a context. In this paper it is proven that for the IKT
statistical model, HIST requires necessarily that $f_{1}$ must be SIED (namely
\textit{stationary}, \textit{isotropic} and \textit{% everywhere-defined}).
This implies, in turn, that the functional form of the PDF is uniquely
prescribed at all times. In particular, it is found that necessarily the PDF
must coincide with an isotropic Gaussian distribution. The conclusion is
relevant for the investigation of the so-called homogenous, isotropic and
stationary turbulence.

22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
2
The categories of this paper are: math
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an