Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singularity formation to the 2D Cauchy problem of the full compressible
  Navier-Stokes equations with zero heat conduction   The formation of singularity and breakdown of strong solutions to the
two-dimensional (2D) Cauchy problem of the full compressible Navier-Stokes
equations with zero heat conduction are considered. It is shown that for the
initial density allowing vacuum, the strong solution exists globally if the
density $\rho$ and the pressure $P$ satisfy
$\|\rho\|_{L^{\infty}(0,T;L^\infty)}+\|P\|_{L^{\infty}(0,T;L^\infty)}<\infty$.
In addition, the initial density can even have compact support. The
logarithm-type estimate for the Lam{\'e} system and some weighted estimates
play a crucial role in the proof.

28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
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
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph