Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Non-uniqueness of continuous entropy solutions to the isentropic
  compressible Euler equations   We consider the Cauchy problem for the isentropic compressible Euler
equations in a three-dimensional periodic domain under general pressure laws.
For any smooth initial density away from the vacuum, we construct infinitely
many entropy solutions with no presence of shock. In particular, the
constructed density is smooth and the momentum is $\alpha$-H\"older continuous
for $\alpha<1/7$. Also, we provide a continuous entropy solution satisfying the
entropy inequality strictly.

16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga