Vlasov-Poisson type systems are well established kinetic models for dilute plasma. The precise structure of the model differs according to which species of charged particle (electrons or ions) it describes, with the most well known version of the system describing electrons. The model for ions, however, has been studied only more recently, owing to an additional exponential nonlinearity in the equation for the electrostatic potential that creates several mathematical difficulties not encountered in the electron case.

Quantitative stability estimates in Wasserstein distances have played a crucial role in the understanding of equations of Vlasov type. I will discuss recent developments in Wasserstein estimates in the context of the ionic Vlasov-Poisson system, including applications to the well-posedness theory, the quasineutral limit (in which the Debye length tends to zero) and the derivation of the equation from a particle system.

Based on joint works with Mikaela Iacobelli (ETH Zürich).