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 plas mas consisting of electrons and ions is presented. The various model equati ons 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 lim it. A rigorous proof of the zero-electron-mass limit in the quasi-hydrodyna mic 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 o f degenerate type is proved without the assumptions needed for the zero-ele ctron-mass limit (essentially, positivity of the particle densities). Final ly, the uniqueness of solutions to the limit problem is studied. (C) 2000 E ditions scientifiques et medicales Elsevier SAS.