Global quasi-neutral limit of Euler-Maxwell systems with velocity dissipation

We consider smooth solutions to the Cauchy problem for an isentropic Euler-Maxwell system with velocity dissipation and small physical parameters. For initial data uniformly close to constant equilibrium states, we prove the global-in-time convergence of the system as the parameters go to zero. The limit systems are the e-MHD system and the incompressible Euler equations, both with velocity dissipation. The proof of the results relies on a single uniform energy estimate with respect to the time and the parameters, together with compactness arguments. For this purpose, the classical energy estimates for the symmetrizable hyperbolic system are not sufficient. We construct a Lyapunov type energy by controlling the divergence and the curl of the velocity, the electric and magnetic fields.