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EN
The stability criterion of a fluid cylinder (density p) embedded into a different fluid (density p¹) is derived and discussed. The model is capillary unstable in the domain 0 p the model is purely unstable for all short and long wavelengths. In m≠0 modes the self-gravitating model is neutrally stable as p = p¹ and ordinary stable as p¹ < p but it is purely unstable as p¹ > p. The streaming destabilizing effect makes the self-gravitating instability worse and shrinks the stable domains. The stability analysis of the model under the combined effect of the capillary and self-gravitating forces is performed analytically and verified numerically. When p¹ < p the capillary force and the axial flow have destabilizing influences but the densities ratio p¹/p has a stabilizing effect on the gravitating instability. If p = p¹ the streaming is destabilizing but the capillary force is strongly stabilizing and could suppress the gravitational instability. When p¹ > p the capillary force improved the gravitational instability and created much domains of stability and moreover the instability of the self-gravitating force disappeared in several cases of axisymmetric disturbances.
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