# American Institute of Mathematical Sciences

September  2009, 2(3): 465-488. doi: 10.3934/krm.2009.2.465

## On long-time behavior of monocharged and neutral plasma in one and one-half dimensions

 1 Department of Mathematics, Indiana University, Bloomington, IN 47405, United States 2 Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, United States 3 Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, United States

Received  March 2009 Revised  June 2009 Published  July 2009

The motion of a collisionless plasma - a high-temperature, low-density, ionized gas - is described by the Vlasov-Maxwell system. In the presence of large velocities, relativistic corrections are meaningful, and when symmetry of the particle densities is assumed this formally becomes the relativistic Vlasov-Poisson system. These equations are considered in one space dimension and two momentum dimensions in both the monocharged (i.e., single species of ion) and neutral cases. The behavior of solutions to these systems is studied for large times, yielding estimates on the growth of particle momenta and a lower bound, uniform-in-time, on norms of the charge density. We also present similar results in the same dimensional settings for the classical Vlasov-Poisson system, which excludes relativistic effects.
Citation: Robert Glassey, Stephen Pankavich, Jack Schaeffer. On long-time behavior of monocharged and neutral plasma in one and one-half dimensions. Kinetic & Related Models, 2009, 2 (3) : 465-488. doi: 10.3934/krm.2009.2.465
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