Acta Mathematica Sinica, English Series

, Volume 33, Issue 5, pp 635–656

Existence, uniqueness and asymptotic behavior for the Vlasov–Poisson system with radiation damping


DOI: 10.1007/s10114-016-6310-9

Cite this article as:
Chen, J., Zhang, X.W. & Gao, R. Acta. Math. Sin.-English Ser. (2017) 33: 635. doi:10.1007/s10114-016-6310-9


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.


Vlasov–Poisson system radiation damping velocity averages weak solution uniqueness 

MR(2010) Subject Classification

35Q83 35L60 82C21 82D10 

Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.College of ScienceZhongyuan University of TechnologyZhengzhouP. R. China
  2. 2.School of Mathematics and StatisticsHuazhong University of Science and TechnologyWuhanP. R. China

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