Stability of Global Maxwellian For Non-Linear Vlasov-Poisson-Fokker-Planck Equations
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 wordsnon-linear Vlasov–Poisson–Fokker–Planck equation global Maxwellian global a priori estimates exponential convergence
2010 MR Subject Classification35H10 76P99 82B21
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