Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global existence of weak solutions to the compressible Navier-Stokes
  equations with temperature-depending viscosity coefficients   This paper is devoted to the global existence of weak solutions to the
three-dimensional compressible Navier-Stokes equations with heat-conducting
effects in a bounded domain. The viscosity and the heat conductivity
coefficients are assumed to be functions of the temperature, and the shear
viscosity coefficient may vanish as the temperature goes to zero. The proof is
to apply Galerkin method to a suitable approximate system with several
parameters and obtain uniform estimates for the approximate solutions. The key
ingredient in obtaining the required estimates is to apply De Giorgi's
iteration to the modified temperature equation, from which we can get a lower
bound for the temperature not depending on the artificial viscosity coefficient
introduced in the modified momentum equation, which makes the compactness
argument available as the artificial viscous term vanishes.

21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th