A hierarchy of hydrodynamic models for plasmas.: Zero-electron-mass limits in the drift-diffusion equations

A model hierarchy of hydrodynamic and quasi-hydrodynamic equations for plasmas consisting of electrons and ions is presented. The various model equations are obtained from the transient Euler-Poisson system for electrons and ions in the zero-electron-mass limit and/or in the zero-relaxation-time limit. A rigorous proof of the zero-electron-mass limit in the quasi-hydrodynamic equations is given. This model consists of two parabolic equations for the electrons and ions and the Poisson equation for the electric potential, subject to initial and mixed boundary conditions, The remaining asymptotic limits will be proved in forthcoming publications. Furthermore, the existence of solutions to the limit problem which can be of degenerate type is proved without the assumptions needed for the zero-electron-mass limit (essentially, positivity of the particle densities). Finally, the uniqueness of solutions to the limit problem is studied. (C) 2000 Editions scientifiques et medicales Elsevier SAS.