Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recent Advances Concerning Certain Class of Geophysical Flows   This paper is devoted to reviewing several recent developments concerning
certain class of geophysical models, including the primitive equations (PEs) of
atmospheric and oceanic dynamics and a tropical atmosphere model. The PEs for
large-scale oceanic and atmospheric dynamics are derived from the Navier-Stokes
equations coupled to the heat convection by adopting the Boussinesq and
hydrostatic approximations, while the tropical atmosphere model considered here
is a nonlinear interaction system between the barotropic mode and the first
baroclinic mode of the tropical atmosphere with moisture.
  We are mainly concerned with the global well-posedness of strong solutions to
these systems, with full or partial viscosity, as well as certain singular
perturbation small parameter limits related to these systems, including the
small aspect ratio limit from the Navier-Stokes equations to the PEs, and a
small relaxation-parameter in the tropical atmosphere model. These limits
provide a rigorous justification to the hydrostatic balance in the PEs, and to
the relaxation limit of the tropical atmosphere model, respectively. Some
conditional uniqueness of weak solutions, and the global well-posedness of weak
solutions with certain class of discontinuous initial data, to the PEs are also
presented.

18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc