Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Formation of singularity and smooth wave propagation for the
  non-isentropic compressible Euler equations   We define compressive and rarefactive waves and give the differential
equations describing smooth wave steepening for the compressible Euler
equations with a varying entropy profile and general pressure laws. Using these
differential equations, we directly generalize P. Lax's singularity (shock)
formation results for hyperbolic systems with two variables to the compressible
Euler equations for a polytropic ideal gas. Our results are valid globally
without restriction on the size of the variation of initial data.

27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph