Communications in Mathematical Sciences

Volume 14 (2016)

Number 1

Global classical solutions of the “one and one-half” dimensional Vlasov–Maxwell–Fokker–Planck system

Pages: 209 – 232

DOI: https://dx.doi.org/10.4310/CMS.2016.v14.n1.a8

Authors

Stephen Pankavich (Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, Colorado, U.S.A.)

Jack Schaeffer (Department of Mathematics Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania, U.S.A.)

Abstract

We study the “one and one-half” dimensional 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 in the large of classical solutions to the Cauchy problem and a gain in regularity of the distribution function in its momentum argument.

Keywords

kinetic theory, Vlasov, Fokker–Planck equation, global existence

2010 Mathematics Subject Classification

35L60, 35Q83, 82C22, 82D10

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Published 16 September 2015