Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Energy conservation for the weak solutions of the compressible
  Navier-Stokes equations   In this paper, we prove the energy conservation for the weak solutions of the
compressible Navier-Stokes equations for any time $t>0$, under certain
conditions. The results hold for the renormalized solutions of the equations
with constant viscosities, as well as the weak solutions of the equations with
degenerate viscosity. Our conditions do not depend on the dimensions. The
energy may conserve on the vacuum for the compressible Navier-Stokes equations
with constant viscosities. Our results are the first ones on the energy
conservation for the weak solutions of the compressible Navier-Stokes
equations.

7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
9
The categories of this paper are: nlin