Asymptotic estimates for an axisymmetric rotating fluid

AbstractA variational method is used to study the shape of a self-gravitating fluid mass rotating with a prescribed angular momentum per unit mass. The model is of primary interest in astrophysics, where it is taken as a model of a star. Sharp estimates are obtained on the diameter of the rotating body in terms of the total mass M and parameter Q = TW; T and W represent, respectively, the kinetic and potential energy. The cases of Q small (slowly rotating body) and Q large (rapidly rotating body) are dealt with separately