Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global wellposed problem for the 3-D incompressible anisotropic
  Navier-Stokes equations   In this paper, we consider a global wellposed problem for the 3-D
incompressible anisotropic Navier-Stokes equations (\textit{ANS}). In order to
do so, we first introduce the scaling invariant Besov-Sobolev type spaces,
$B^{-1+\frac{2}{p},{1/2}}_{p}$ and $B^{-1+\frac{2}{p},{1/2}}_{p}(T)$, $p\geq2$.
Then, we prove the global wellposedness for (\textit{ANS}) provided the initial
data are sufficient small compared to the horizontal viscosity in some suitable
sense, which is stronger than $B^{-1+\frac{2}{p},{1/2}}_{p}$ norm. In
particular, our results imply the global wellposedness of (\textit{ANS}) with
high oscillatory initial data.

10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph