Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the well-posedness of the inviscid multi-layer quasi-geostrophic
  equations   The inviscid multi-layer quasi-geostrophic equations are considered over an
arbitrary bounded domain. The no-flux but non-homogeneous boundary conditions
are imposed to accommodate the free fluctuations of the top and layer
interfaces. Using the barotropic and baroclinic modes in the vertical
direction, the elliptic system governing the streamfunctions and the potential
vorticity is decomposed into a sequence of scalar elliptic boundary value
problems, where the regularity theories from the two-dimensional case can be
applied. With the initial potential vorticity being essentially bounded, the
multi-layer quasi-equations are then shown to be globally well-posed, and the
initial and boundary conditions are satisfied in the classical sense.

36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci