Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A priori estimates for the motion of a self-gravitating incompressible
  liquid with free surface boundary   In this paper, we prove a priori estimates in Lagrangian coordinates for the
equations of motion of an incompressible, inviscid, self-gravitating fluid with
free boundary. The estimates show that on a finite time interval we control
five derivatives of the fluid velocity and five and a half derivatives of the
coordinates of the moving domain.

9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th