Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large time behavior of solutions to the $3$D anisotropic Navier-Stokes
  equation   We consider the large time behavior of the solution to the $3$D Navier-Stokes
equation with horizontal viscosity $\Delta_{\rm h} u=\partial_1^2
u+\partial_2^2 u$ and show that the $L^p$ decay rate of the horizontal
components of the velocity field coinsides to that of the $2$D heat kernel,
while the vertical component decays like the $3$D heat kernel. Moreover, we
consider the asymptotic expansion of the solution and find that a portion of
the nonlinear term affect the leading term of the horizontal components of the
velocity field, whereas the leading term of the vertical component is given by
only the linear solution.

27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th