The Zero-Electron-Mass Limit in the Hydrodynamic Model (Euler-Poisson System)

The aim of this paper is the study of the relaxation limit of the 3-D bipolar hydrodynamic model for semiconductors. We prove the convergence for the weak solutions to the bipolar Euler–Poisson system towards the solutions to the bipolar drifthyphen;diffusion system, as the relaxation time tends to zero.

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Existence and zero-electron-mass limit of strong solutions to the stationary compressible Navier-Stokes-Poisson equation with large external force

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.4634 ◽

2017 ◽

Author(s):

Yeping Li ◽

Jie Liao

Keyword(s):

Poisson Equation ◽

External Force ◽

Strong Solutions ◽

Navier Stokes ◽

Electron Mass ◽

Mass Limit

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The zero-electron-mass limit for a stationary nonisentropic hydrodynamic semiconductor model

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2008.01.081 ◽

2008 ◽

Vol 343 (2) ◽

pp. 871-883 ◽

Cited By ~ 1

Author(s):

Yeping Li ◽

Jizhou Zhang

Keyword(s):

Electron Mass ◽

Mass Limit

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ASYMPTOTIC EXPANSIONS IN A STEADY STATE EULER–POISSON SYSTEM AND CONVERGENCE TO INCOMPRESSIBLE EULER EQUATIONS

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202505000546 ◽

2005 ◽

Vol 15 (05) ◽

pp. 717-736 ◽

Cited By ~ 4

Author(s):

YUE-JUN PENG ◽

INGRID VIOLET

Keyword(s):

Steady State ◽

Euler Equations ◽

Asymptotic Expansions ◽

Electron Mass ◽

Poisson System ◽

Drift Diffusion Model ◽

Drift Diffusion ◽

Incompressible Euler Equations ◽

Potential Flows ◽

Incompressible Euler

This work is concerned with a steady state Euler–Poisson system for potential flows arising in mathematical modeling for plasmas and semiconductors. We study the zero electron mass limit and zero relaxation time limit of the system by using the method of asymptotic expansions. These two limits are expressed by the Maxwell–Boltzmann relation and the classical drift-diffusion model, respectively. For each limit, we show the existence and uniqueness of profiles and justify the asymptotic expansions up to any order. These results also give new approaches for the convergence of the Euler–Poisson system to incompressible Euler equations, which has already been obtained via the quasi-neutral limit.

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