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We summarize the general formalism describing surface flows inthree-dimensional space in a form which is suitable for various astrophysicalapplications. We then apply the formalism to the analysis of non-radialperturbations of self-gravitating spherical fluid shells.  Spherically symmetric gravitating shells (or bubbles) have been used innumerous model problems especially in general relativity and cosmology. Aradially oscillating shell was recently suggested as a model for a variablecosmic object. Within Newtonian gravity we show that self-gravitating staticfluid shells are unstable with respect to linear non-radial perturbations. Onlyshells (bubbles) with a negative mass (or with a charge the repulsion of whichis compensated by a tension) are stable.Comment: 20 pages, to be published in the Astrophysical Journal, typos  correcte

Self‐gravitating Fluid Shells and Their Nonspherical Oscillations in Newtonian Theory