Acta Mathematica Scientia

, Volume 39, Issue 1, pp 127–138 | Cite as

Stability of Global Maxwellian For Non-Linear Vlasov-Poisson-Fokker-Planck Equations

  • Jie Liao (廖杰)Email author
  • Qianrong Wang (王倩蓉)
  • Xiongfeng Yang (杨雄锋)


In this article, we establish the exponential time decay of smooth solutions around a global Maxwellian to the non-linear Vlasov–Poisson–Fokker–Planck equations in the whole space by uniform-in-time energy estimates. The non-linear coupling of macroscopic part and Fokker–Planck operator in the model brings new difficulties for the energy estimates, which is resolved by adding tailored weighted-in-v energy estimates suitable for the Fokker–Planck operator.

Key words

non-linear Vlasov–Poisson–Fokker–Planck equation global Maxwellian global a priori estimates exponential convergence 

2010 MR Subject Classification

35H10 76P99 82B21 


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Copyright information

© Wuhan Institutes of Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  • Jie Liao (廖杰)
    • 1
    Email author
  • Qianrong Wang (王倩蓉)
    • 1
  • Xiongfeng Yang (杨雄锋)
    • 2
  1. 1.Department of MathematicsEast China University of Science and TechnologyShanghaiChina
  2. 2.School of Mathematical Sciences; Key Laboratory of Scientific and Engineering Computing (MOE)Shanghai Jiao Tong UniversityShanghaiChina

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