Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on optimal decay rates for the axisymmetric D-solutions to the
  steady Navier-Stokes equations   In this paper, we investigate the decay properties of an axisymmetric
D-solutions to stationary incompressible Navier-Stokes systems in
$\mathbb{R}^3$. We obtain the optimal decay rate $|{\bf u}(x)|\leq
\frac{C}{|x|+1}$ for axisymmetric flows without swirl. Furthermore, we find a
dichotomy for the decay rates of the swirl component $u_{\theta}$, that is,
either $O(\frac{1}{r+1})\leq |u_{\theta}(r,z)|\leq
\frac{C\log(r+1)}{(r+1)^{1/2}}$ or $|u_{\theta}(r,z)|\leq \frac{C
r}{(\rho+1)^3}$, where $\rho=\sqrt{r^2+z^2}$. In the latter case, we can
further deduce that the other two components of the velocity field also attain
the optimal decay rates: $|u_r(r,z)|+ |u_{z}(r,z)|\leq \frac{C}{\rho+1}$. We do
not require any small assumptions on the forcing term.

19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio