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

TL;DR

This paper proves the global existence, uniqueness, and convergence to equilibrium of solutions for the Vlasov-Poisson-Landau system with Coulomb interaction in three-dimensional space, assuming initial data is close to equilibrium.

Contribution

It establishes the first rigorous results on global well-posedness and long-term behavior for this complex kinetic system with Coulomb interactions.

Findings

Global existence and uniqueness of solutions.

Quantitative convergence rates to Maxwellian equilibrium.

Applicable to initial data close to equilibrium.

Abstract

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