Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the ill/well-posedness and nonlinear instability of the
  magneto-geostrophic equations   We consider an active scalar equation that is motivated by a model for
magneto-geostrophic dynamics and the geodynamo. We prove that the non-diffusive
equation is ill-posed in the sense of Hadamard in Sobolev spaces. In contrast,
the critically diffusive equation is well-posed. In this case we give an
example of a steady state that is nonlinearly unstable, and hence produces a
dynamo effect in the sense of an exponentially growing magnetic field.

34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th