Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the long time behavior of compressible fluid flows excited by random
  forcing   We are concerned with the long time behavior of the stochastic Navier--Stokes
system for compressible fluids in dimension two and three. In this setting, the
part of the phase space occupied by the solution depends sensitively on the
choice of the initial state. Our main results are threefold. (i) The kinetic
energy of a solution is universally and asymptotically bounded, independent of
the initial datum. (ii) Time shifts of a solution with initially controlled
energy are asymptotically compact and generate an entire solution defined for
all $t\in R$. (iii) Every solution with initially controlled energy generates a
stationary solution and even an ergodic stationary solution on the closure of
the convex hull of its $\omega$--limit set.

30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th