We revisit the classic problem of the stability of drops and jets held by
surface tension, while regarding the compressibility of bulk fluids and spatial
dimensions as free parameters. By mode analysis, it is shown that there exists
a critical compressibility above which the drops (and disks) become unstable
for a spherical perturbation. For a given value of compressibility (and those
of the surface tension and density at the equilibrium), this instability
criterion provides a minimal radius below which the drop cannot be a stable
equilibrium. According to the existence of the above unstable mode of drop,
which corresponds to a homogeneous perturbation of cylindrical jet, the
dispersion relation of Rayleigh-Plateau instability for cylinders drastically
changes. In particular, we identify another critical compressibility above
which the homogeneous unstable mode is predominant. The analysis is done for
non-relativistic and relativistic perfect fluids, of which self-gravity is
ignored.Comment: 24 pages, 5 figures, 1 table; v2: typos corrected; v3: final version
to appear in JF
