Global solutions of certain plasma fluid models in three-dimension

We consider several dispersive time-reversible plasma fluid models in 3 dimensions: the Euler-Poisson 2-fluid model, the relativistic Euler–Maxwell 1-fluid model, and the relativistic Euler–Maxwell 2-fluid model. In all of these models, we prove global stability of the constant background solutions, in the sense that small, smooth, and irrotational perturbations lead to smooth global solutions that decay as t → ∞.