The Vlasov-Poisson-Landau System with the Specular-Reflection Boundary Condition

2020/10/11 by Dong, Hongjie, Guo, Yan, Ouyang, Zhimeng · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2010.05314

Abstract

We consider the Vlasov-Poisson-Landau system, a classical model for a dilute collisional plasma interacting through Coulombic collisions and with its self-consistent electrostatic field. We establish global stability and well-posedness near the Maxwellian equilibrium state with decay in time and some regularity results for small initial perturbations, in any general bounded domain (including a torus as in a tokamak device), in the presence of specular reflection boundary condition. We provide a new improved L²→ L^∞ framework: L² energy estimate combines only with S^p estimate for the ultra-parabolic equation.

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• Hydrodynamic limit of the Vlasov-Poisson-Fokker-Planck system in low-field regime
• Global existence for the relativistic Vlasov-Poisson system in a two-dimensional bounded domain

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