Existence, Uniqueness and Asymptotic Behavior for the Vlasov-Poisson System with Radiation Damping

We investigate the Cauchy problem for the Vlasov-Poisson system with radiation damping. By virtue of energy estimate and a refined velocity average lemma, we establish the global existence of nonnegative weak solution and asymptotic behavior under the condition that initial data have finite mass and energy. Furthermore, by building a Gronwall inequality about the distance between the Lagrangian flows associated to the weak solutions, we can prove the uniqueness of weak solution when the initial data have a higher order velocity moment.