J. Differential Eqns. 99, 59 - 77 (1992)

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

G. Rein, J. Weckler¹

1) Mathematisches Institut der Universität München, Theresienstr. 39, 80333 München, Germany


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 corollary 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.
Gerhard Rein (rein@rz.mathematik.uni-muenchen.de)