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

Abstract

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 quasi-neutral 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.