On the Vlasov-Poisson-Fokker-Planck equation near Maxwellian
Hyung Ju Hwang, Juhi Jang
TL;DR
This paper proves that small smooth solutions to the Vlasov-Poisson-Fokker-Planck equations decay exponentially over time to the Maxwellian distribution, using energy estimates and macroscopic equations in both unbounded and periodic domains.
Contribution
It establishes the exponential decay rate for solutions to the Vlasov-Poisson-Fokker-Planck equations near Maxwellian, a result not previously demonstrated.
Findings
Exponential decay rate of solutions proven
Decay holds in both whole space and periodic domains
Energy estimates and macroscopic equations are key tools
Abstract
We establish the exponential time decay rate of smooth solutions of small amplitude to the Vlasov-Poisson-Fokker-Planck equations to the Maxwellian both in the whole space and in the periodic box via the uniform-in-time energy estimates and also the macroscopic equations.
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Taxonomy
TopicsGas Dynamics and Kinetic Theory · Advanced Thermodynamics and Statistical Mechanics · Statistical Mechanics and Entropy