The Relative Energy for Electromagnetic Fluids

This note introduces the relative energy for two-species electromagnetic fluid models. The relative energy identity for a bipolar Euler-Maxwell system is formally derived. Moreover, two applications of the relative energy for these type of systems are given. The first application deals with the weak-strong uniqueness property of a Euler-Poisson system, while the second concerns the relaxation limit of a bipolar Euler-Poisson system towards a bipolar drift-diffusion system.