Maximal estimates for the Fokker-Planck operator with strong magnetic field
Zeinab Karaki
TL;DR
This paper establishes maximal estimates for the Vlasov-Fokker-Planck operator under strong magnetic fields using a nilpotent approach and Lie algebra representations, improving the understanding of its domain.
Contribution
It introduces a novel nilpotent approach and Lie algebra representation technique to derive maximal estimates for the operator with strong magnetic fields.
Findings
Maximal estimate derived for the Vlasov-Fokker-Planck operator
Enhanced characterization of the operator's domain
Application of Lie algebra representation in PDE analysis
Abstract
We consider the Vlasov-Fokker-Planck operator with a strong external magnetic field. We show a maximal type estimate on this operator using a nilpotent approach on vector field polynomial operators and including the notion of representation on a Lie algebra. This estimate makes it possible to give a better characterization of the domain of the closure of the considered operator.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Gas Dynamics and Kinetic Theory · Stochastic processes and financial applications