The Vlasov-Poisson-Landau System in ${\mathbb{R}}_x^3$

Abstract

For the Landau-Poisson system with Coulomb interaction in ${\mathbb{R}}_x^3$, we prove the global existence, uniqueness, and large time convergence rates to the Maxwellian equilibrium for solutions which start out sufficiently close.

50 pages

References in corpus (3)

• Global Classical Solutions of the Boltzmann Equation without Angular Cut-off
• Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials
• Global solutions to the Vlasov-Poisson-Landau System

Cited by in corpus (16)

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• Global mild solutions of the Landau and non-cutoff Boltzmann equations
• The Vlasov-Poisson-Boltzmann system without angular cutoff
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• The Vlasov-Poisson-Boltzmann system for a disparate mass binary mixture
• Regularity of the Vlasov-Poisson-Boltzmann System without angular cutoff
• Uniqueness of Bounded Solutions for the Homogeneous Relativistic Landau Equation with Coulomb Interactions
• Low Regularity Solutions for the Vlasov-Poisson-Landau/Boltzmann System
• Small Knudsen rate of convergence to rarefaction wave for the Landau equation
• Entropy dissipation estimates for the relativistic Landau equation, and applications
• Smoothing Estimates of the Vlasov-Poisson-Landau System
• Asymptotics toward viscous contact waves for solutions of the Landau equation
• Spectral gap formation to kinetic equations with soft potentials in bounded domain
• Global solution and time decay of the Vlasov-Poisson-Landau system in R3
• Global smooth dynamics of a fully ionized plasma with long-range collisions
• The Vlasov-Poisson-Boltzmann/Landau system with polynomial perturbation near Maxwellian