Stability of the Equilibrium to the Vlasov-Poisson-Boltzmann System with Non-constant Background Charge

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Abstract

We study the global existence of classical solution to the Vlasov-Poisson-Boltzmann system with non-constant background charge. In this case the local Maxwellian is the unique stationary state. We show that this equilibrium is nonlinear stable provided that the initial perturbation is sufficient small. Our result solves an open problem stated by Duan and Yang (SIAM J. Math. Anal. 41(6):2353–2387, 2009) in one dimensional case.

Keywords

Vlasov-Poisson-Boltzmann system Non-constant background charge Stability 

Mathematics Subject Classification

76P05 82C40 35B35 

Notes

Acknowledgements

The authors are very grateful to the referees for their helpful suggestions, which improved the earlier version of this paper. Yang is supported by the Fundamental Research Funds for the Central Universities (Grant No. NS2012122). Li is supported by the Fundamental Research Funds for the Central Universities (Grant No. 56XZA14010).

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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, College of ScienceNanjing University of Aeronautics and AstronauticsNanjingP.R. China

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