A one-dimensional kinetic model of plasma dynamics with a transport field

Charles Nguyen; Stephen Pankavich

doi:10.3934/eect.2014.3.681

Article Contents

2014, Volume 3, Issue 4: 681-698. Doi: 10.3934/eect.2014.3.681

This issue Previous Article On a class of elliptic operators with unbounded diffusion coefficients Next Article On the threshold for Kato's selfadjointness problem and its $L^p$-generalization

A one-dimensional kinetic model of plasma dynamics with a transport field

Charles Nguyen^1, and
Stephen Pankavich^2,

1.
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019
2.
Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO 80002

Received: December 31, 2013

Revised: March 31, 2014

Published: November 2014

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Abstract

Motivated by the fundamental model of a collisionless plasma, the Vlasov-Maxwell (VM) system, we consider a related, nonlinear system of partial differential equations in one space and one momentum dimension. As little is known regarding the regularity properties of solutions to the non-relativistic version of the (VM) equations, we study a simplified system which also lacks relativistic velocity corrections and prove local-in-time existence and uniqueness of classical solutions to the Cauchy problem. For special choices of initial data, global-in-time existence of these solutions is also shown. Finally, we provide an estimate which, independent of the choice of initial data, yields additional global-in-time regularity of the associated field.

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

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References

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