Système Euler-Poisson non linéaire. Existence globale de solutions faibles entropiques

An asymptotic preserving scheme for the two-fluid Euler–Poisson model in the quasineutral limit

“…The terms $f i , $f e denote the divergence of the tensors f e and f i . The mathematical theory of the Euler-Poisson system has been investigated in [12,56] for the isothermal case and in [49] for the isentropic case.…”

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

“…The mathematical study of Euler-Poisson systems for plasmas has attracted a lot of attention in the mathematical literature since several years (see, e.g., [4,5,[20][21][22][23][24][25]). In order to perform numerical simulations of the hyperbolic equations, a lot of computing power and special algorithms are needed [9,12].…”

Zero-relaxation-time limits in the hydrodynamic equations for plasmas revisited

“…The Euler-Poisson systems for plasmas have been intensively studied in the literature both analytically and numerically (see, e.g., [2,3,6,11,14]). In the zero-relaxation-time limit, the model equations can be approximated by the driftdiffusion equations, which are much simpler to treat, e.g.…”

“…The existence of global weak entropy solutions to (6)-(8) is proved in [3] for γ e = γ i = 1, and in [13] for γ i > 1. In the second case, the following assumptions are needed :…”