Global existence of Lagrangian solutions to the ionic Vlasov--Poisson system

Abstract

In this paper, we study the Cauchy problem of the ionic Vlasov--Poisson (IVP) system for a broad class of initial data. To this end, we establish well-posedness and stability estimates for the Poisson--Boltzmann equation $-\Delta \Phi =\rho -e^{\Phi }$ provided $\rho \in L_{+}^p$ with $p>1$, whereas previous approaches required $p>\frac{d}{2}$. Building upon these results, we construct global-in-time renormalized/Lagrangian solutions to the IVP system.

Revised abstract and the structure of the paper. Corrected some minor errors. Added new references and remarks