Separated characteristics and global solvability for the one and one-half dimensional Vlasov Maxwell system

Robert Glassey; Stephen Pankavich; Jack Schaeffer

doi:10.3934/krm.2016003

Article Contents

2016, Volume 9, Issue 3: 455-467. Doi: 10.3934/krm.2016003

This issue Previous Article Convergence of the full compressible Navier-Stokes-Maxwell system to the incompressible magnetohydrodynamic equations in a bounded domain Next Article Global nonlinear stability of rarefaction waves for compressible Navier-Stokes equations with temperature and density dependent transport coefficients

Separated characteristics and global solvability for the one and one-half dimensional Vlasov Maxwell system

1.
Department of Mathematics, Indiana University, Bloomington, IN 47405
2.
Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO 80002
3.
Department of Mathematics Sciences, Carnegie Mellon University, Pittsburgh, PA 15213

Received: August 31, 2015

Revised: December 31, 2015

Published: August 2016

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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 $\vert v_1 \vert = 1$. Additionally, for initial particle distributions that are even in the second velocity argument $v_2$, the global-in-time existence of solutions is shown.

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Mathematics Subject Classification: Primary: 35L60, 35Q83, 35Q99; Secondary: 82C21, 82C22, 82D10.

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