Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Delta shocks and vacuum states for the isentropic magnetogasdynamics
  equations for Chaplygin gas as pressure and magnetic field vanish   This paper is concerned with the Riemann problem for the isentropic Chaplygin
gas magnetogasdynamics equations and the formation of delta shocks and vacuum
states as pressure and magnetic field vanish. Firstly, the Riemann problem of
the isentropic magnetogasdynamics equations for Chaplygin gas is solved
analytically. Secondly, it is rigorously proved that, as both the pressure and
the magnetic field vanish, the Riemann solution containing two shock waves
tends to a delta shock solution to the transport equations, and the
intermediate density between the two shocks tends to a weighted
$\delta$-measure which forms the delta shock; while the Riemann solution
containing two rarefaction waves tends to a two-contact-discontinuity solution
to the transport equations, the termediate state between the two contact
discontinuities is a vacuum state.

19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics