Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of conservation laws of compressible isentropic fluid
  flow in n>1 spatial dimensions   For the Euler equations governing compressible isentropic fluid flow with a
barotropic equation of state (where pressure is a function only of the
density), local conservation laws in $n>1$ spatial dimensions are fully
classified in two primary cases of physical and analytical interest: (1)
kinematic conserved densities that depend only on the fluid density and
velocity, in addition to the time and space coordinates; (2) vorticity
conserved densities that have an essential dependence on the curl of the fluid
velocity. A main result of the classification in the kinematic case is that the
only equation of state found to be distinguished by admitting extra
$n$-dimensional conserved integrals, apart from mass, momentum, energy, angular
momentum and Galilean momentum (which are admitted for all equations of state),
is the well-known polytropic equation of state with dimension-dependent
exponent $\gamma=1+2/n$. In the vorticity case, no distinguished equations of
state are found to arise, and here the main result of the classification is
that, in all even dimensions $n\geq 2$, a generalized version of Kelvin's
two-dimensional circulation theorem is obtained for a general equation of
state.

17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
1
The categories of this paper are: cs
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat