Geodesic
Global solutions of the Euler–Maxwell two-fluid system in 3D
Yan Guo1 ; Alexandru D. Ionescu2 ; Benoit Pausader3
1 Division of Applied Mathematics, Brown University, Providence, RI
2 Department of Mathematics, Princeton University, Princeton, NJ
3 Université Paris 13, Sorbonne Paris Cité, LAGA, CNRS (UMR 7539), Villetaneuse, France
Annals of mathematics, Tome 183 (2016) no. 2, pp. 377-498.

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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.
DOI : 10.4007/annals.2016.183.2.1

Yan Guo 1 ; Alexandru D. Ionescu 2 ; Benoit Pausader 3

1 Division of Applied Mathematics, Brown University, Providence, RI
2 Department of Mathematics, Princeton University, Princeton, NJ
3 Université Paris 13, Sorbonne Paris Cité, LAGA, CNRS (UMR 7539), Villetaneuse, France 
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Yan Guo; Alexandru D. Ionescu; Benoit Pausader. Global solutions of the Euler–Maxwell two-fluid system in 3D. Annals of mathematics, Tome 183 (2016) no. 2, pp. 377-498. doi : 10.4007/annals.2016.183.2.1. http://geodesic.mathdoc.fr/articles/10.4007/annals.2016.183.2.1/

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