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 electron fluids interact with their own self-consistent electromagnetic field. We prove global stability of a constant neutral background, in the sense that...

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Bibliographic Details
Published in:Annals of mathematics 2016-03, Vol.183 (2), p.377-498
Main Authors: Guo, Yan, Ionescu, Alexandru D., Pausader, Benoit
Format: Article
Language:English
Subjects:
Integration by parts
Ions
Klein Gordon equation
Logical proofs
Mathematics
Nonlinearity
Orthogonality
Resonance
Spacetime
Wave equations
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Summary: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.
ISSN:0003-486X
DOI:10.4007/annals.2016.183.2.1