Global solutions of the Euler-Maxwell two-fluid system in 3D

The fundamental two-fluid model for describing plasma dynamics is given by the Euler-Maxwell system, in which compressible ion and elec-tron uids interact with their own self-consistent electromagnetic field. We prove global stability of a constant neutral background, in the sense that irrotational, smooth and localized perturbations of a constant background with small amplitude lead to global smooth solutions in three space di-mensions for the Euler-Maxwell system. Our construction is robust in dimension 3 and applies equally well to other plasma models such as the Euler-Poisson system for two-fluids and a relativistic Euler-Maxwell sys-tem for two fluids. Our solutions appear to be the first nontrivial global smooth solutions in all of these models.