Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global well-posedness of the 2D nonhomogeneous incompressible nematic
  liquid crystal flows with vacuum   This paper concerns the Cauchy problem of the two-dimensional (2D)
nonhomogeneous incompressible nematic liquid crystal flows on the whole space
$\mathbb{R}^{2}$ with vacuum as far field density. It is proved that the 2D
nonhomogeneous incompressible nematic liquid crystal flows admits a unique
global strong solution provided the initial data density and the gradient of
orientation decay not too slow at infinity, and the initial orientation
satisfies a geometric condition (see \eqref{eq1.3}). In particular, the initial
data can be arbitrarily large and the initial density may contain vacuum states
and even have compact support. As a byproduct, the large time behavior of the
solution is also obtained.

35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph