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

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 $L^2\to L^{\infty }$ framework: $L^2$ energy estimate combines only with $S^p$ estimate for the ultra-parabolic equation.

51 pages

Cited by in corpus (2)

• Global $L_p$ estimates for kinetic Kolmogorov-Fokker-Planck equations in nondivergence form
• Global strong solutions to the Vlasov-Poisson-Boltzmann system with soft potential in a bounded domain