Existence, uniqueness and asymptotic behavior for the Vlasov–Poisson system with radiation damping
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- Chen, J., Zhang, X.W. & Gao, R. Acta. Math. Sin.-English Ser. (2017) 33: 635. doi:10.1007/s10114-016-6310-9
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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.