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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[added]
Y. Guo, A. D. Ionescu, and B. Pausader, "Global solutions of certain plasma fluid models in three-dimension," J. Math. Phys., vol. 55, p. 12, 2014.@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},
YEAR={2014},
PAGES={no.~12, 123102, 26 pp.},
MRNUMBER={3390554},
zblnumber = {1308.76340},
doi = {10.1063/1.4903254},
} -
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