Separated Characteristics and Global Solvability for the one and one-half dimensional Vlasov Maxwell System

TL;DR

This paper analyzes the one-and-a-half dimensional Vlasov-Maxwell system, establishing bounds on particle distribution supports, derivative estimates, and proving global existence of solutions under certain symmetry conditions.

Contribution

It provides new bounds, derivative estimates, and a global existence proof for the VM system without relativistic assumptions in a simplified setting.

Findings

Bounds on spatial and velocity supports of the distribution function

Uniform derivative estimates away from critical velocities

Global-in-time existence for symmetric initial distributions

Abstract

The motion of a collisionless plasma - a high-temperature, low-density, ionized gas - is described by the Vlasov-Maxwell (VM) system. These equations are considered in one space dimension and two momentum dimensions without the assumption of relativistic velocity corrections. The main results are bounds on the spatial and velocity supports of the particle distribution function and uniform estimates on derivatives of this function away from the critical velocity $| v_1 | = 1$. Additionally, for initial particle distributions that are even in the second velocity argument $v_2$, the global-in-time existence of solutions is shown.