Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The viscous surface-internal wave problem: global well-posedness and
  decay   We consider the free boundary problem for two layers of immiscible, viscous,
incompressible fluid in a uniform gravitational field, lying above a general
rigid bottom in a three-dimensional horizontally periodic setting. We establish
the global well-posedness of the problem both with and without surface tension.
We prove that without surface tension the solution decays to the equilibrium
state at an almost exponential rate; with surface tension, we show that the
solution decays at an exponential rate. Our results include the case in which a
heavier fluid lies above a lighter one, provided that the surface tension at
the free internal interface is above a critical value, which we identify. This
means that sufficiently large surface tension stabilizes the Rayleigh-Taylor
instability in the nonlinear setting. As a part of our analysis, we establish
elliptic estimates for the two-phase stationary Stokes problem.

16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th