Abstract
The capillary stability of a liquid cylinder of radius R-0 surrounded by a tenuous medium has been investigated for all modes of perturbations and the self-gravitating incompressible gas cylinder embedded in a gravitational medium in axisymmetric and non-axisymmetric disturbances is studied. The gravitational stability of a hollow jet under the combination of the forces self-gravitating and capillary forces has been developed. A general dispersion relation is derived. The capillary force is destabilizing for small domain the axisymmetric made while it is stabilizing in all the rest. The capillary instability is depressed and then stability sets in. In the present work, the self-gravitating instability of capillary streaming annular gas-fluid jet has been developed for all perturbation modes. The problem is formulated analytically, solved numerically and the stability criterion is derived and discussed.