Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global existence and decay for solutions of the Hele-Shaw flow with
  injection   We study the global existence and decay to spherical equilibrium of Hele-Shaw
flows with surface tension. We prove that without injection of fluid,
perturbations of the sphere decay to zero exponentially fast. On the other
hand, with a time-dependent rate of fluid injection into the Hele-Shaw cell,
the distance from the moving boundary to an expanding sphere (with
time-dependent radius) also decays to zero but with an algebraic rate, which
depends on the injection rate of the fluid.

15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci