Global dynamics in the 3D pressureless Euler-Poisson system for ions

Abstract: In this work we consider the pressureless Euler-Poisson system on $\mathbb{R}^3$ describing ion dynamics, which is a common model in the study of cold plasma. We prove global regularity and scattering for small, irrotational velocity fields around a constant density profile. At the heart of the result is a dispersive mechanism leading to amplitude decay at the full rate in $3$D. This fast decay feature and a favourable structure of the nonlinearity allow to control quadratic interactions globally.