Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of the planar rarefaction wave to two-dimensional compressible
  Navier-Stokes equations   It is well-known that the rarefaction wave, one of the basic wave patterns to
the hyperbolic conservation laws, is nonlinearly stable to the one-dimensional
compressible Navier-Stokes equations (cf. [14,15,12,17]). In the present paper
we proved the time-asymptotically nonlinear stability of the planar rarefaction
wave to the two-dimensional compressible and isentropic Navier-Stokes
equations, which gives the first stability result of the planar rarefaction
wave to the multi-dimensional system with physical viscosities.

36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol