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arXiv · 2103.12276

Large friction-high force fields limit for the nonlinear Vlasov--Poisson--Fokker--Planck system

José A. Carrillo·Young-Pil Choi·Yingping Peng
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Abstract

We provide a quantitative asymptotic analysis for the nonlinear Vlasov--Poisson--Fokker--Planck system with a large linear friction force and high force-fields. The limiting system is a diffusive model with nonlocal velocity fields often referred to as aggregation-diffusion equations. We show that a weak solution to the Vlasov--Poisson--Fokker--Planck system strongly converges to a strong solution to the diffusive model. Our proof relies on the modulated macroscopic kinetic energy estimate based on the weak-strong uniqueness principle together with a careful analysis of the Poisson equation.

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José A. Carrillo, Young-Pil Choi, Yingping Peng. 2021-03-23. Large friction-high force fields limit for the nonlinear Vlasov--Poisson--Fokker--Planck system. https://arxiv.org/abs/2103.12276

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