Hall–MHD System as a Simplified One-Fluid Ion Model Derived from Two-Fluid Euler–Maxwell Equations

We derive the one-fluid ion model from the partial-compressible two-fluid Euler-Maxwell system with collision mechanism in which the ions are considered compressible while electrons are not. Deriving such a model based solely on the zero-electron-mass limit or the quasi-neutral limit is quite open because of the singularities of the electric field and the strong coupling effects of the Lorentz forces. In this work, we apply the combined zero-electron-mass and quasi-neutral limit. We prove the global-in-time existence and the combined limit of smooth solutions. Furthermore, for well-prepared initial data, we establish the error estimates of the convergence between smooth solutions to one-fluid and two-fluid models. It is worth mentioning that the velocities of ions and electrons are different in this study.