Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariant manifolds and the long-time asymptotics of the Navier-Stokes
  and vorticity equations on R^2   We construct finite-dimensional invariant manifolds in the phase space of the
Navier-Stokes equation on R^2 and show that these manifolds control the
long-time behavior of the solutions. This gives geometric insight into the
existing results on the asymptotics of such solutions and also allows one to
extend those results in a number of ways.

17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys