Global solution and time decay of the Vlasov-Poisson-Landau system in R3

TL;DR

This paper establishes the existence and decay properties of global solutions to the Vlasov-Poisson-Landau system in three-dimensional space, revealing optimal decay rates for densities and faster decay for potential and disparity between species.

Contribution

It constructs the unique global solution near Maxwellian in R3 and analyzes decay rates, extending understanding of the system's long-term behavior.

Findings

Global solutions exist and are unique near Maxwellian.

Total density decays at optimal algebraic rates.

Disparity and electric potential decay faster in periodic settings.

Abstract

We construct the global unique solution near a global Maxwellian to the Vlasov-Poisson-Landau system in the whole space. The total density of two species of particles decays at the optimal algebraic rates as the Landau equation in the whole space, but the disparity between two species and the electric potential decay at the faster rates as the Vlasov-Poisson-Landau system in a periodic box.