Global classical solutions for the 'One and one-half'' dimensional relativistic Vlasov-Maxwell-Fokker-Planck system

Stephen Pankavich; Nicholas Michalowski

doi:10.3934/krm.2015.8.169

Article Contents

2015, Volume 8, Issue 1: 169-199. Doi: 10.3934/krm.2015.8.169

This issue Previous Article Global magnetic confinement for the 1.5D Vlasov-Maxwell system Next Article

Global classical solutions for the "One and one-half'' dimensional relativistic Vlasov-Maxwell-Fokker-Planck system

Stephen Pankavich^1, and
Nicholas Michalowski^2,

1.
Department of Applied Mathematics and Statistics, Colorado School of Mines, 1500 Illinois St, Golden, CO 80401
2.
Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003

Received: April 30, 2014

Revised: July 31, 2014

Published: February 2015

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Abstract

In a recent paper Calogero and Alcántara [Kinet. Relat. Models, 4 (2011), pp. 401-426] derived a Lorentz-invariant Fokker-Planck equation, which corresponds to the evolution of a particle distribution associated with relativistic Brownian Motion. We study the ``one and one-half'' dimensional version of this problem with nonlinear electromagnetic interactions - the relativistic Vlasov-Maxwell-Fokker-Planck system - and obtain the first results concerning well-posedness of solutions. Specifically, we prove the global-in-time existence and uniqueness of classical solutions to the Cauchy problem and a gain in regularity of the distribution function in its momentum argument.

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

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