Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Remarks on the free boundary problem of compressible Euler equations in
  physical vacuum with general initial densities   In this paper, we establish a priori estimates for the three-dimensional
compressible Euler equations with moving physical vacuum boundary, the
$\gamma$-gas law equation of state for $\gamma=2$ and the general initial
density $\ri \in H^5$. Because of the degeneracy of the initial density, we
investigate the estimates of the horizontal spatial and time derivatives and
then obtain the estimates of the normal or full derivatives through the
elliptic-type estimates. We derive a mixed space-time interpolation inequality
which play a vital role in our energy estimates and obtain some extra estimates
for the space-time derivatives of the velocity in $L^3$.

5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an