Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entire vortex solutions of negative degree for the anisotropic
  Ginzburg-Landau system   The anisotropic Ginzburg-Landau system \[ \Delta u+\delta\, \nabla
(\mathrm{div}\: u) +\delta\, \mathrm{curl}^*(\mathrm{curl}\: u)=(|u|^2-1) u, \]
for $u\colon\mathbb R^2\to\mathbb R^2$ and $\delta\in (-1,1)$, models the
formation of vortices in liquid crystals. We prove the existence of entire
solutions such that $|u(x)|\to 1$ and $u$ has a prescribed topological degree
$d\leq -1$ as $|x|\to\infty$, for small values of the anisotropy parameter
$|\delta| < \delta_0(d)$. Unlike the isotropic case $\delta=0$, this cannot be
reduced to a one-dimensional radial equation. We obtain these solutions by
minimizing the anisotropic Ginzburg-Landau energy in an appropriate class of
equivariant maps, with respect to a finite symmetry subgroup.

17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex