The Euler-Maxwell two-fluid system in 3D

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 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.

108 pages

References in corpus (3)

• Global Smooth Ion Dynamics in the Euler-Poisson System
• Derivation of the Zakharov equations
• Numerical approximation of the Euler-Maxwell model in the quasineutral limit

Cited by in corpus (4)

• Bilinear dispersive estimates via space-time resonances, part II: dimensions 2 and 3
• Global analysis of a model for capillary water waves in 2D
• From bipolar Euler-Poisson system to unipolar Euler-Poisson system in the perspective of mass
• Large time behavior for the non-isentropic Navier-Stokes-Maxwell system