Guo, Yan; Ionescu, Alexandru D.; Pausader, Benoit Global solutions of the Euler-Maxwell two-fluid system in 3D. (English) Zbl 1345.35075 Ann. Math. (2) 183, No. 2, 377-498 (2016). The results obtained in this article are related to the Euler-Maxwell system, that represents the two-fluid model describing plasma dynamics. This model is a system of nonlinear hyperbolic conservation laws with no dissipation and no relaxation effects. The authors develop a method that can be used for complicated physical coupled systems, at least in dimension 3. The global dynamics of the solutions to the Euler-Maxwell system is analyzed by means of dispersive analysis combined with energy estimates, relying on the Fourier transform. It is proved that irrotational, smooth and localized perturbations of a constant background with small amplitude lead to global smooth solutions for the 3D Euler-Maxwell system. The proposed method can be extended to other quasilinear problems in 3D and the constructed solutions represent the first smooth, nontrivial global solutions. Reviewer: Ruxandra Stavre (Bucureşti) Cited in 65 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 76X05 Ionized gas flow in electromagnetic fields; plasmic flow 35Q60 PDEs in connection with optics and electromagnetic theory 35B65 Smoothness and regularity of solutions to PDEs 35L65 Hyperbolic conservation laws Keywords:dispersive analysis; Euler-Maxwell two-fluid model; global regularity; space-time resonances; the Fourier transform method × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] 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. · Zbl 1308.76340 · doi:10.1063/1.4903254 [2] S. 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