Global solutions of the Euler-Maxwell two-fluid system in 3D (Q280104)

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.