Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Development of singularities for the compressible Euler equations with
  external force in several dimensions   We consider solutions to the Euler equations in the whole space from a
certain class, which can be characterized, in particular, by finiteness of
mass, total energy and momentum. We prove that for a large class of right-hand
sides, including the viscous term, such solutions, no matter how smooth
initially, develop a singularity within a finite time. We find a sufficient
condition for the singularity formation, "the best sufficient condition", in
the sense that one can explicitly construct a global in time smooth solution
for which this condition is not satisfied "arbitrary little". Also compactly
supported perturbation of nontrivial constant state is considered. We
generalize the known theorem by Sideris on initial data resulting in
singularities. Finally, we investigate the influence of frictional damping and
rotation on the singularity formation.

19
The categories of this paper are: eess
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex