Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Local existence of solution to free boundary value problem for
  compressible Navier-Stokes equations
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th