On global classical solutions of the Vlasov-Poisson system with radiation damping

We are concerned with global well-posedness of the three-dimensional Vlasov-Poisson system with radiation damping. First, we show that global C-1 solutions verifying specified decay conditions are stable under small perturbations. As a consequence, we obtain that a small perturbation of a monopolar and spherically symmetric plasma launches a global C-1 solution that preserves quasi-spherical symmetry at the macroscopic level. Second, we show that an initially quasineutral datum with C-1 regularity launches a global classical solution that propagates quasi-neutrality at the macroscopic level. Finally, we obtain better decay estimates for the radiation damping in both cases.