Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On solutions of the 2D Navier-Stokes equations with constant energy and
  enstrophy   It is not yet known if the global attractor of the space periodic 2D
Navier-Stokes equations contains nonstationary solutions $u(x,t)$ such that
their energy and enstrophy per unit mass are constant for every $t \in
(-\infty, \infty)$. The study of the properties of such solutions was initiated
in \cite{CMM13}, where, due to the hypothetical existence of such solutions,
they were called "ghost solutions". In this work, we introduce and study
geometric structures shared by all ghost solutions. This study led us to
consider a subclass of ghost solutions for which those geometric structures
have a supplementary stability property. In particular, we show that the wave
vectors of the active modes of this subclass of ghost solutions must satisfy
certain supplementary constraints. We also found a computational way to check
for the existence of these ghost solutions.

29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org