Stability of disk-like galaxies : Part I: Stability via reduction

We prove the existence and stability of flat steady states of the Vlasov-Poisson system, which in astrophysics are used as models of disk-like galaxies. We follow the variational approach developed by Guo and Rein [5, 6, 7] for this type of problems and extend previous results of Rein [11]. In particular, we employ a reduction procedure which relates the stability problem for the Vlasov-Poisson system to the analogous question for the Euler-Poisson system.