Communications in Mathematical Sciences

Volume 15 (2017)

Number 2

The quasineutral limit of the Vlasov–Poisson equation in Wasserstein metric

Pages: 481 – 509



Daniel Han-Kwan (CMLS, École polytechnique, CNRS, Université Paris-Saclay, Palaiseau, France)

Mikaela Iacobelli (DPMMS Centre for Mathematical Sciences, University of Cambridge, United Kingdom)


In this work, we study the quasineutral limit of the one-dimensional Vlasov–Poisson equation for ions with massless thermalized electrons. We prove new weak-strong stability estimates in the Wasserstein metric that allow us to extend and improve previously known convergence results. In particular, we show that given a possibly unstable analytic initial profile, the formal limit holds for sequences of measure initial data converging sufficiently fast in the Wasserstein metric to this profile. This is achieved without assuming uniform analytic regularity.


Vlasov–Poisson system, Wasserstein stability estimates, quasineutral limit

2010 Mathematics Subject Classification

35B35, 35Q83

Published 21 February 2017