Asymptotic growth and decay of two-dimensional symmetric plasmas

Ben-Artzi, Jonathan ORCID: https://orcid.org/0000-0001-6184-9313, Morisse, Baptiste and Pankavich, Stephen 2024. Asymptotic growth and decay of two-dimensional symmetric plasmas. Kinetic and Related Models 17 (1) , pp. 29-51. 10.3934/krm.2023015

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Abstract

We study the large time behavior of classical solutions to the two-dimensional Vlasov-Poisson (VP) and relativistic Vlasov-Poisson (RVP) systems launched by radially-symmetric initial data with compact support. In particular, we prove that particle positions and momenta grow unbounded as and obtain sharp rates on the maximal values of these quantities on the support of the distribution function for each system. Furthermore, we establish nearly sharp rates of decay for the associated electric field, as well as upper and lower bounds on the decay rate of the charge density in the large time limit. We prove that, unlike (VP) in higher dimensions, smooth solutions do not scatter to their free-streaming profiles as because nonlinear, long-range field interactions dominate the behavior of characteristics due to the exchange of energy from the potential to the kinetic term. In this way, the system may "forget" any previous configuration of particles.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	American Institute of Mathematical Sciences (AIMS)
ISSN:	1937-5093
Date of First Compliant Deposit:	13 June 2023
Date of Acceptance:	16 March 2023
Last Modified:	06 Dec 2023 01:07
URI:	https://orca.cardiff.ac.uk/id/eprint/160320

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