Abstract
The fundamental “two-fluid” model for describing plasma dynamics is given by the Euler–Maxwell system, in which compressible ion and electron fluids 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 dimensions 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 system for two fluids. Our solutions appear to be the first nontrivial global smooth solutions in all of these models.
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