Acta mathematica scientia,Series B ›› 2023, Vol. 43 ›› Issue (2): 668-674.doi: 10.1007/s10473-023-0212-6

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THE ENERGY CONSERVATION OF VLASOV-POISSON SYSTEMS*

Jingpeng, Wu, Xianwen Zhang   

  1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
  • Received:2021-12-07 Revised:2022-03-31 Online:2023-03-25 Published:2023-04-12
  • Contact: †Xianwen ZHANG, E-mail: xwzhang@hust.edu.cn.
  • About author:Jingpeng Wu, E-mail: d201980015@hust.edu.cn
  • Supported by:
    This work was supported by the National Natural Science Foundation of China (11871024).

Abstract: We prove that energy conservation holds for weak solutions to classical Vlasov-Poisson systems with proper regularity. In particular, there exists a solution that conserves energy with $|v|^mf_0\in L^1_{x,v}$ for $m>9/4$.

Key words: Vlasov-Poisson system, weak solutions, energy conservation

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