Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On formation of singularity of the full compressible magnetohydrodynamic
  equations with zero heat conduction   We are concerned with the formation of singularity and breakdown of strong
solutions to the Cauchy problem of the three-dimensional full compressible
magnetohydrodynamic equations with zero heat conduction. It is proved that for
the initial density allowing vacuum, the strong solution exists globally if the
deformation tensor $\mathfrak{D}(\mathbf{u})$ and the pressure $P$ satisfy
$\|\mathfrak{D}(\mathbf{u})\|_{L^{1}(0,T;L^\infty)}+\|P\|_{L^{\infty}(0,T;L^\infty)}<\infty$.
In particular, the criterion is independent of the magnetic field. The
logarithm-type estimate for the Lam{\'e} system and some delicate energy
estimates play a crucial role in the proof.

35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex