Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a differential equation for a gas bubbles collapse mathematical model   In this paper we present a mathematical model for estimate the collapse time
of a gas bubble in a vane of a oil gerotor pump. This amount of time cannot be
greater of the total time spent by the pump for filling and then emptying out a
vane in a single revolution, otherwise there is a loss of lubrication between
internal and external gears. We assume that oil is incompressible and viscous,
the bubble has a spherical shape and it is not translating into the external
fluid. The analytical treatment of the model shows that the Navier-Stokes
equations for the velocity field of the oil can be reduced to a single non
linear ordinary differential equation for the variation in time of the bubble
radius. The collapse time estimated by a numerical resolution of this equation
and the collapse time calculated from an analytical resolution of the
linearized equation are substantially equal.

11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex