Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global solutions of 3D incompressible MHD system with mixed partial
  dissipation and magnetic diffusion near an equilibrium   This paper focuses on the 3D incompressible magnetohydrodynamic (MHD)
equations with mixed partial dissipation and magnetic diffusion. Our main
result assesses the global stability of perturbations near the steady solution
given by a background magnetic field. The stability problem on the MHD
equations with partial or no dissipation has attracted considerable interests
recently and there are substantial developments. The new stability result
presented here is among the very few stability conclusions currently available
for ideal or partially dissipated MHD equations. As a special consequence of
the techniques introduced in this paper, we obtain the small data global
well-posedness for the 3D incompressible Navier-Stokes equations without
vertical dissipation.

5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an