Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long-time Behavior of a Two-layer Model of Baroclinic Quasi-geostrophic
  Turbulence   We study a viscous two-layer quasi-geostrophic beta-plane model that is
forced by imposition of a spatially uniform vertical shear in the eastward
(zonal) component of the layer flows, or equivalently a spatially uniform
north-south temperature gradient. We prove that the model is linearly unstable,
but that non-linear solutions are bounded in time by a bound which is
independent of the initial data and is determined only by the physical
parameters of the model. We further prove, using arguments first presented in
the study of the Kuramoto-Sivashinsky equation, the existence of an absorbing
ball in appropriate function spaces, and in fact the existence of a compact
finite-dimensional attractor, and provide upper bounds for the fractal and
Hausdorff dimensions of the attractor. Finally, we show the existence of an
inertial manifold for the dynamical system generated by the model's solution
operator. Our results provide rigorous justification for observations made by
Panetta based on long-time numerical integrations of the model equations.

23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio