Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a non-solenoidal approximation to the incompressible Navier-Stokes
  equations   We establish an asymptotic profile that sharply describes the behavior as
$t\to\infty$ for solutions to a non-solenoidal approximation of the
incompressible Navier-Stokes equations introduced by Temam. The solutions of
Temam's model are known to converge to the corresponding solutions of the
classical Navier-Stokes, e.g., in $L^3\_{\rm loc} (R^+ \times R^3)$, provided
$\epsilon\to0$, where $\epsilon>0$ is the physical parameter related to the
artificial compressibility term. However, we show that such model is no longer
a good approximation of Navier-Stokes for large times: indeed, its solutions
can decay much slower as $t\to+\infty$ than the corresponding solutions of
Navier-Stokes.

29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph