Zero-electron-mass limit and zero-relaxation-time limit in a multi-dimensional stationary bipolar Euler–Poisson system

2013 ◽  
Vol 219 (10) ◽  
pp. 5174-5184
Author(s):  
Xuemin Zhang ◽  
Yeping Li
Keyword(s):  
Relaxation Time ◽  
Time Limit ◽  
Electron Mass ◽  
Poisson System ◽  
Mass Limit

Vanishing electron mass limit in the bipolar Euler–Poisson system

2011 ◽  
Vol 12 (2) ◽  
pp. 1002-1012 ◽  
Author(s):  
Li Chen ◽  
Xiuqing Chen ◽  
Chunlei Zhang
Keyword(s):  
Electron Mass ◽  
Poisson System ◽  
Mass Limit

The zero-electron-mass limit in the Euler–Poisson system for both well- and ill-prepared initial data

Nonlinearity ◽  
2011 ◽  
Vol 24 (10) ◽  
pp. 2745-2761 ◽  
Author(s):  
Giuseppe Alì ◽  
Li Chen
Keyword(s):  
Initial Data ◽  
Electron Mass ◽  
Poisson System ◽  
Mass Limit

scholarly journals On the Vanishing Electron-Mass Limit in Plasma Hydrodynamics in Unbounded Media

2012 ◽  
Vol 22 (6) ◽  
pp. 985-1012 ◽  
Author(s):  
Donatella Donatelli ◽  
Eduard Feireisl ◽  
Antonín Novotný
Keyword(s):  
Electron Mass ◽  
Mass Limit ◽  
Unbounded Media ◽  
Plasma Hydrodynamics

Instability of a viscous coflowing jet in a radial electric field

2008 ◽  
Vol 596 ◽  
pp. 285-311 ◽  
Author(s):  
FANG LI ◽  
XIE-YUAN YIN ◽  
XIE-ZHEN YIN
Keyword(s):  
Relaxation Time ◽  
Electric Field ◽  
Thin Layer ◽  
Euler Number ◽  
Radial Electric Field ◽  
Dispersion Relations ◽  
Time Limit ◽  
Liquid Viscosity ◽  
Electrical Relaxation ◽  
Thin Layer Approximation

A temporal linear instability analysis of a charged coflowing jet with two immiscible viscous liquids in a radial electric field is carried out for axisymmetric disturbances. According to the magnitude of the liquid viscosity relative to the ambient air viscosity, two generic cases are considered. The analytical dimensionless dispersion relations are derived and solved numerically. Two unstable modes, namely the para-sinuous mode and the para-varicose mode, are identified in the Rayleigh regime. The para-sinuous mode is found to always be dominant in the jet instability. Liquid viscosity clearly stabilizes the growth rates of the unstable modes, but its effect on the cut-off wavenumber is negligible. The radial electric field has a dual effect on the modes, stabilizing them when the electrical Euler number is smaller than a critical value and destabilizing them when it exceeds that value. Moreover, the electrical Euler number and Weber number increase the dominant and cut-off wavenumbers significantly. Based on the Taylor–Melcher leaky dielectric theory, two limit cases, i.e. the small electrical relaxation time limit (SERT) and the large electrical relaxation time limit (LERT), are discussed. For coflowing jets having a highly conducting outer liquid, SERT may serve as a good approximation. In addition, the dispersion relations under the thin layer approximation are derived, and it is concluded that the accuracy of the thin layer approximation is closely related to the values of the dimensionless parameters.

scholarly journals Zero-electron-mass limit of Euler-Poisson equations

2013 ◽  
Vol 33 (10) ◽  
pp. 4743-4768 ◽  
Author(s):  
Jiang Xu ◽  
◽  
Ting Zhang ◽  
Keyword(s):  
Electron Mass ◽  
Mass Limit ◽  
Poisson Equations

Global zero-relaxation limit of the non-isentropic Euler–Poisson system for ion dynamics

2020 ◽  
Vol 120 (3-4) ◽  
pp. 301-318
Author(s):  
Yuehong Feng ◽  
Xin Li ◽  
Shu Wang
Keyword(s):  
Relaxation Time ◽  
Energy Estimates ◽  
Ion Dynamics ◽  
Poisson System ◽  
Smooth Solutions ◽  
Drift Diffusion ◽  
Limit System ◽  
Momentum Relaxation ◽  
Global Zero ◽  
Compactness Arguments

This paper is concerned with smooth solutions of the non-isentropic Euler–Poisson system for ion dynamics. The system arises in the modeling of semi-conductor, in which appear one small parameter, the momentum relaxation time. When the initial data are near constant equilibrium states, with the help of uniform energy estimates and compactness arguments, we rigorously prove the convergence of the system for all time, as the relaxation time goes to zero. The limit system is the drift-diffusion system.

The relaxation-time limit in the compressible Euler–Maxwell equations

2011 ◽  
Vol 74 (18) ◽  
pp. 7005-7011 ◽  
Author(s):  
Jianwei Yang ◽  
Shu Wang ◽  
Juan Zhao
Keyword(s):  
Relaxation Time ◽  
Maxwell Equations ◽  
Time Limit ◽  
Compressible Euler

scholarly journals The relaxation-time limit in the quantum hydrodynamic equations for semiconductors

2006 ◽  
Vol 225 (2) ◽  
pp. 440-464 ◽  
Author(s):  
Ansgar Jüngel ◽  
Hai-Liang Li ◽  
Akitaka Matsumura
Keyword(s):  
Relaxation Time ◽  
Time Limit ◽  
Hydrodynamic Equations ◽  
Quantum Hydrodynamic ◽  
Quantum Hydrodynamic Equations
Sign in / Sign up

Export Citation Format

Share Document