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)