Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and stability of stationary solutions to the compressible
  quantum model   In this paper, the compressible quantum model with the given mass source and
the external force of general form in three-dimensional whole space is
considered. Based on the weighted $L^2$ method and $L^\infty$ estimates, the
existence and uniqueness of stationary solutions can be obtained by the
contraction mapping principle. By using a general energy method, the nonlinear
stability of stationary solutions is studied, and the time decay rates of the
solutions are established when the initial perturbation belongs to
$\dot{H}^{-s}$ with $0 \leq s < \frac{3}{2}$.

35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph