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September 10, 2025

Global strong solution and diffusive limit of the two-species Vlasov–Poisson–Boltzmann system

WWWeijun WuNanchang University FZFujun ZhouSouth China University of Technology WGWeihua GongGuangdong University Of Finances and Economics

Key Points

A global strong solution is constructed for the two-species Vlasov–Poisson–Boltzmann system in three dimensions.
The analysis includes a new Hx,v2−Wx,v1,∞ framework, utilizing weighted energy estimates to prove the results.
Results validate the rigorous transition to the incompressible Navier–Stokes–Fourier–Poisson limit under cutoff hard potentials.
The findings are uniformly valid across the Knudsen number range, from 0 to 1, showcasing significant behavior in fluid dynamics.

Abstract

In this paper, we investigate global strong solution and diffusive limit of the two-species Vlasov–Poisson–Boltzmann system in R3 for the full range of cutoff hard potentials 0 ≤ γ ≤ 1. By introducing a new Hx,v2−Wx,v1,∞ framework, which is based on the interplay between the velocity weighted Hx,v2 energy estimate and the time-velocity weighted Wx,v1,∞-estimate for the two-species Vlasov–Poisson–Boltzmann system, we construct the global weighted estimate uniformly in the Knudsen number ɛ ∈ (0, 1]. As a result, global strong solution is constructed and the two-fluid incompressible Navier–Stokes–Fourier–Poisson limit is rigorously justified for all cutoff hard potentials 0 ≤ γ ≤ 1.

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Cite This Study

Wu et al. (Fri,) studied this question.

synapsesocial.com/papers/68c1b81f54b1d3bfb60ec536 https://doi.org/https://doi.org/10.1063/5.0243706

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