Variational method for stable polytropic galaxies (Q1971515)

The author considers the problem of dynamical stability of polytropic galaxies under spherically and non-spherically symmetric perturbations. It is well known that the Vlasov-Poisson equations describing the mechanical state of a stellar system have global classical solution and a family of stationary solutions which depend on the particle energy. There are many investigations of stability of these stationary solutions. Recently it was shown via a dual variational method that the stationary solutions corresponding to polytropic galaxies are stable under symmetric perturbations. Here the author introduces a new compactness argument which allows to give a simple direct proof of dynamical stability of polytropic galaxies under sperically and non-spherically symmetric perturbations.