Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Smooth global Lagrangian flow for the 2D Euler and second-grade fluid
  equations   We present a very simple proof of the global existence of a $C^\infty$
Lagrangian flow map for the 2D Euler and second-grade fluid equations (on a
compact Riemannian manifold with boundary) which has $C^\infty$ dependence on
initial data $u_0$ in the class of $H^s$ divergence-free vector fields for
$s>2$.

7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin