Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the local well--posedness of the two component $b$-family of
  equations   In this paper we consider the two component $b$-family of equations on
$\mathbb R$. We write the equations on a Sobolev type diffeomorphism group. As
an application of this formulation we show that the dependence on the initial
data is nowhere locally uniformly continuous. In particular it is nowhere
locally Lipschitz and nowhere locally H\"older continuous.

17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys