Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-gravitating fluid dynamics, unstabilities and solitons   This work studies the hydrodynamics of self-gravitating compressible
isothermal fluids. We show that the hydrodynamic evolution equations in absence
of viscosity are scale covariant. We study the evolution of the time dependent
fluctuations around singular and regular isothermal spheres. We linearize the
fluid equations around such stationary solutions and apply Laplace transform to
solve them. We find that the system is stable below a critical size (X ~ 9.0 in
dimensionless variables) and unstable above; this size is the same critical
size found in the study of the thermodynamical stability in the canonical
ensemble and associated to a center-to-border density ratio of 32.1 . We prove
that the value of this critical size is independent of the Reynolds number of
the system. Furthermore, we give a detailed description of the series of
successive dynamical instabilities that appear at higher and higher sizes
following the geometric progression X_n ~ 10.7^n. We turn then to study exact
solutions of the hydrodynamic equations without viscosity and we provide
analytic and numerical axisymmetric soliton-type solutions. The stability of
exact solutions corresponding to a collapsing filament is studied by computing
linear fluctuations. Radial fluctuations growing faster than the background are
found for all sizes of the system. However, a critical size (X ~ 4.5) appears,
separating a weakly from a strongly unstable regime.

32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys