Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On classical solutions to the Cauchy problem of the 2D compressible
  non-resistive MHD equations with vacuum   In this paper, we investigate the Cauchy problem of the compressible
non-resistive MHD on $\mathbb{R}^2$ with vacuum as far field density. We prove
that the 2D Cauchy problem has a unique local strong solution provided the
initial density and magnetic field decay not too slow at infinity. Furthermore,
if the initial data satisfies some additional regularity and compatibility
conditions, the strong solution becomes a classical one. Additionally, we
establish a blowup criterion for the 2D compressible non-resistive MHD
depending solely on the density and magnetic fields.

27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs