Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on spherically symmetric isentropic compressible flows with
  density-dependent viscosity coefficients   In this note, by constructing suitable approximate solutions, we prove the
existence of global weak solutions to the compressible Navier-Stokes equations
with density-dependent viscosity coefficients in the whole space
$\mathbb{R}^N$, $N\geq2$ (or exterior domain), when the initial data are
spherically symmetric. In particular, we prove the existence of spherically
symmetric solutions to the Saint-Venant model for shallow water in the whole
space (or exterior domain).

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The categories of this paper are: astro-ph
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio