Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of Rarefaction Waves to the 1D Compressible Navier-Stokes
  Equations with Density-dependent Viscosity   In this paper, we study the asymptotic stability of rarefaction waves for the
compressible isentropic Navier-Stokes equations with density-dependent
viscosity. First, a weak solution around a rarefaction wave to the Cauchy
problem is constructed by approximating the system and regularizing the initial
values which may contain vacuum state. Then some global in time estimates on
the weak solution are obtained. Based on these uniform estimates, the vacuum
states are shown to vanish in finite time and the weak solution we constructed
becomes a unique strong one. Consequently, the stability of the rarefaction
wave is proved in a weak sense. The theory holds for large-amplitudes
rarefaction waves and arbitrary initial perturbations.

13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con