The Vlasov-Poisson-Boltzmann System for Soft Potentials

2011/12/07 by Renjun Duan, Tong Yang, Duan, Renjun +3 · 1 citation
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1112.1453

openalex publication_date 2011/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An important physical model describing the dynamics of dilute weakly ionized plasmas in the collisional kinetic theory is the Vlasov-Poisson-Boltzmann system for which the plasma responds strongly to the self-consistent electrostatic force. This paper is concerned with the electron dynamics of kinetic plasmas in the whole space when the positive charged ion flow provides a spatially uniform background. We establish the global existence and optimal convergence rates of solutions near a global Maxwellian to the Cauchy problem on the Vlasov-Poisson-Boltzmann system for angular cutoff soft potentials with -2≤ γ<0. The main idea is to introduce a time dependent weight function in the velocity variable to capture the singularity of the cross-section at zero relative velocity.

Cited by

• The non-cutoff Vlasov-Poisson-Boltzmann system with weak collisions

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