On time decay for the spherically symmetric Vlasov-Poisson system

Jack Schaeffer

doi:10.3934/krm.2021021

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2022, Volume 15, Issue 4: 721-727. Doi: 10.3934/krm.2021021

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On time decay for the spherically symmetric Vlasov-Poisson system

Jack Schaeffer

Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA, https://www.cmu.edu/math/people/faculty/schaeffer-j.html

In memory of Robert Glassey

Received: March 31, 2021

Published: August 2022

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Abstract

A collisionless plasma is modeled by the Vlasov-Poisson system. Solutions in three space dimensions that have smooth, compactly supported initial data with spherical symmetry are considered. An improved field estimate is presented that is based on decay estimates obtained by Illner and Rein. Then some estimates are presented that ensure only particles with sufficiently small velocity can be found within a certain (time dependent) ball.

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

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References

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