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Global solutions of the Euler-Maxwell two-fluid system in 3D. (English) Zbl 1345.35075
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.

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
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