Global solutions of 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 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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    @article{added, MRKEY={3390554},
      author = {Guo, Yan and Ionescu, A. D. and Pausader, B.},
      TITLE={ Global solutions of certain plasma fluid models in three-dimension},
      JOURNAL={J. Math. Phys.},
      VOLUME={55},
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Authors

Yan Guo

Division of Applied Mathematics, Brown University, Providence, RI

Alexandru D. Ionescu

Department of Mathematics, Princeton University, Princeton, NJ

Benoit Pausader

Université Paris 13, Sorbonne Paris Cité, LAGA, CNRS (UMR 7539), Villetaneuse, France

Current address:

Brown University, Providence, RI