Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Formation of singularities in solutions to the compressible radiation
  hydrodynamics equations with vacuum   We study the Cauchy problem for multi-dimensional compressible radiation
hydrodynamics equations with vacuum. First, we present some sufficient
conditions on the blow-up of smooth solutions in multi-dimensional space. Then,
we obtain the invariance of the support of density for the smooth solutions
with compactly supported initial mass density by the property of the system
under the vacuum state. Based on the above-mentioned results, we prove that we
cannot get a global classical solution, no matter how small the initial data
are, as long as the initial mass density is of compact support. Finally, we
will see that some of the results that we obtained are still valid for the
isentropic flows with degenerate viscosity coefficients as well as 1-D case.

33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph