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.
Jie LIAO
,
Qianrong WANG
,
Xiongfeng YANG
. STABILITY OF GLOBAL MAXWELLIAN FOR NON-LINEAR VLASOV-POISSON-FOKKER-PLANCK EQUATIONS[J]. Acta mathematica scientia, Series B, 2019
, 39(1)
: 127
-138
.
DOI: 10.1007/s10473-019-0112-y
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