Abstract
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.
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The authors would like to thank anonymous referees for their valuable suggestions concerning the presentation of this paper.
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Chen, J., Zhang, X.W. & Gao, R. Existence, uniqueness and asymptotic behavior for the Vlasov–Poisson system with radiation damping. Acta. Math. Sin.-English Ser. 33, 635–656 (2017). https://doi.org/10.1007/s10114-016-6310-9
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DOI: https://doi.org/10.1007/s10114-016-6310-9