About Linear Stability for Multiple Gas Balls

The results presented in this paper are generalizations of earlier work on the linear stability of non-rotating round gas balls in equilibrium, with respect to perturbations with zero angular momentum. Here we allow a more general barotropic equation of state for the gas, a non-zero angular momentum of the equilibrium state, and we are considering arbitrary numbers of gas balls, intending to use the result later to prove non-linear stability. The result requires an energy stability condition, which we verify for a single, slowly rotating gas ball, and the restricted class of equations of state used in earlier papers.