The evolution of an axi-symmetric Stokes bubble is considered when the bubble volume is changed. Linear stability analysis shows that an expanding spherical bubble is stable, while a shrinking spherical bubble is unstable. Numerical calculations of the time evolution shows that for certain initial condition, such a bubble can form cusps or near cusps or undergo topological change (pinching) bef...

We prove general nonlinear stability and existence theorems for rotating star solutions which are axi-symmetric steady-state solutions of the compressible isentropic EulerPoisson equations in 3 spatial dimensions. We apply our results to rotating and nonrotating white dwarf, and rotating high density supermassive (extreme relativistic) stars, stars which are in convective equilibrium and have u...