Self-gravitating fluid shells and their non-spherical oscillations in Newtonian theory

We summarize the general formalism describing surface flows in three-dimensional space in a form which is suitable for various astrophysical applications. We then apply the formalism to the analysis of non-radial perturbations of self-gravitating spherical fluid shells. Spherically symmetric gravitating shells (or bubbles) have been used in numerous model problems especially in general relativity and cosmology. A radially oscillating shell was recently suggested as a model for a variable cosmic object. Within Newtonian gravity we show that self-gravitating static fluid shells are unstable with respect to linear non-radial perturbations. Only shells (bubbles) with a negative mass (or with a charge the repulsion of which is compensated by a tension) are stable.