Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compressible Navier-Stokes equation with BV initial data: Part II.
  Global stability   In previous work \cite{W-Y-Z-local}, we studied the local well-posedness of
weak solution to the 1-D full compressible Navier-Stokes equation with initial
data of small total variation. Specifically, the local existence, the
regularity, and the uniqueness in certain function space of the weak solution
have been established. The basis for the previous study is the precise
construction of fundamental solution for heat equation with BV conductivity. In
this paper, we continue to investigate the global stability and the time
asymptotic behavior of the weak solution. The main step is to construct the
``effective Green's function'', which is the combination of the heat kernel
with BV coefficient in short time and the Green's function around constant
state in long time. The former one captures the quasi-linear nature of the
system, while the latter one respects the dissipative structure. Then the weak
solution is written into an integral system in terms of this ``effective
Green's function'', and the time asymptotic behavior is established based on a
priori estimate.

16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org