Generic global classical solutions of the Vlasov-Fokker-Planck-Poisson system in three dimensions

Abstract

It is shown that global classical solutions of the Vlasov-Fokker-Planck-Poisson system, for which the field decays in an appropriate way for large times, are generic in the following sense: sufficiently small perturbations of the initial data yield another global solution with the same type of asymptotic behaviour. As a corollay one obtains global existence for small and for nearly neutral initial data. On the way to the global perturbation result sufficient conditions for global existence and a local perturbation result are established.