Stability of the one-species Vlasov-Poisson-Boltzmann system?

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

36 Scopus Citations
View graph of relations


Related Research Unit(s)


Original languageEnglish
Pages (from-to)2353-2387
Journal / PublicationSIAM Journal on Mathematical Analysis
Issue number6
Publication statusPublished - 2009


In this paper, we are concerned with the one-species Vlasov-Poisson- Boltzmann system with a nonconstant background density in full space. There exists a stationary solution when the background density is a small perturbation of a positive constant state. We prove the nonlinear stability of solutions to the Cauchy problem near the stationary state in some Sobolev space without any time derivatives. This result is nontrivial even when the background density is a constant state. In the proof, the macroscopic balance laws are essentially used to deal with the a priori estimates on both the microscopic and macroscopic parts of the solution. Moreover, some interactive energy functionals are introduced to overcome difficulty stemming from the absence of time derivatives in the energy functional. © 2009 Society for Industrial and Applied Mathematics.

Research Area(s)

  • Energy estimates, Stability, Vlasov-Poisson-Boltzmann system