Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global Existence of Solutions to the Compressible Euler Equations with
  Time-dependent Damping and Logarithmic State Equation   In mathematical physics, the pressure function is determined by the equation
of state. There are two existing barotropic state equations: the state equation
for polytropic gas with adiabatic index greater than or equal to 1 and the
state equation for generalized Chaplygin gas in cosmology. In this paper, a
logarithmic pressure is derived naturally with the coexistence of the two
existing state equations through an equivalent symmetric hyperbolic
transformation. On the study of the logarithmic pressure, global existence of
solutions with small initial data to the one-dimensional compressible Euler
equations with time-dependent damping is established.

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The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat