Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear Rayleigh-Taylor Instability for Nonhomogeneous Incompressible
  Viscous Magnetohydrodynamic Flows   We investigate the nonlinear instability of a smooth Rayleigh-Taylor
steady-state solution (including the case of heavier density with increasing
height) to the three-dimensional incompressible nonhomogeneous
magnetohydrodynamic (MHD) equations of zero resistivity in the presence of a
uniform gravitational field. We first analyze the linearized equations around
the steady-state solution. Then we construct solutions of the linearized
problem that grow in time in the Sobolev space $H^k$, thus leading to the
linear instability. With the help of the constructed unstable solutions of the
linearized problem and a local well-posedness result of smooth solutions to the
original nonlinear problem, we establish the instability of the density, the
horizontal and vertical velocities in the nonlinear problem. Moreover, when the
steady magnetic field is vertical and small, we prove the instability of the
magnetic field. This verifies the physical phenomenon: instability of the
velocity leads to the instability of the magnetic field through the induction
equation.

21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc