Communications in Mathematical Sciences

Volume 17 (2019)

Number 4

On large time behavior for the cylindrically symmetric Vlasov–Poisson system

Pages: 1061 – 1069



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


A collisionless plasma is modeled by the Vlasov-Poisson system. Solutions in three space dimensions that have smooth, compactly supported initial data with cylindrical symmetry are considered. Using an identity of Rein and Illner (alt. Perthame) it is shown that almost every characteristic of the Vlasov equation (i.e. almost every particle) “escapes” to infinity for large time.


collisionless plasma, Vlasov–Poisson, cylindrical symmetry

2010 Mathematics Subject Classification

35L60, 35Q83, 82C22, 82D10

Received 3 January 2019

Accepted 23 March 2019

Published 25 October 2019