Global smooth dynamics of a fully ionized plasma with long-range collisions

TL;DR

This paper proves the global existence and convergence rates of solutions near Maxwellians for the Vlasov-Maxwell-Landau system with Coulomb collisions, addressing long-range interactions in plasma physics.

Contribution

It establishes the first global existence results for the system with Coulomb potential using a novel energy method that handles long-range collisions and electromagnetic regularity loss.

Findings

Global solutions exist near Maxwellians for Coulomb collisions.

Convergence rates of solutions are quantitatively obtained.

The method handles dispersion, singularity, and regularity-loss in the system.

Abstract

The motion of a fully ionized plasma of electrons and ions is generally governed by the Vlasov-Maxwell-Landau system. We prove the global existence of solutions near Maxwellians to the Cauchy problem of the system for the long-range collision kernel of soft potentials, particularly including the classical Coulomb collision, provided that initial data is smooth enough and decays in velocity variable fast enough. As a byproduct, the convergence rates of solutions are also obtained. The proof is based on the energy method through designing a new temporal energy norm to capture different features of this complex system such as dispersion of the macro component in $\mathbb{R}^3$, singularity of the long-range collisions and regularity-loss of the electromagnetic field.