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

• 成果类型: Article
• 署名作者: Guo, Yan; Ionescu, Alexandru D.; Pausader, Benoit
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2016.183.2.1
• 发表日期: 2016
• 页码: 377-498
• 关键词: klein-gordon equations; quasi-neutral limit; poisson system; cauchy-problem; wave-equations; space-time; EXISTENCE; derivation

摘要

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.