Communications in Mathematical Sciences
Volume 15 (2017)
The quasineutral limit of the Vlasov–Poisson equation in Wasserstein metric
Pages: 481 – 509
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