Stability of the constant states in the augmented Born–Infeld system

In this paper, we consider the Born–Infeld system, arising as a nonlinear model of electromagnetism, and its extension introduced by Brenier [Hydrodynamic structure of the augmented Born–Infeld equations, Arch. Ration. Mech. Anal. 172(1) (2004) 65–91] the so-called “augmented Born–Infeld system”. We show that this system enjoys a non-resonance structure and prove global existence and linear asymptotic behavior of small (admissible) perturbations of arbitrary constant states.