scholarly journals Quasineutral limit for the compressible two-fluid Euler–Maxwell equations for well-prepared initial data

2020 ◽  
Vol 28 (2) ◽  
pp. 879-895
Author(s):  
Min Li ◽  
◽  
Xueke Pu ◽  
Shu Wang ◽  
◽  
...  
Keyword(s):  
Initial Data ◽  
Maxwell Equations ◽  
Quasineutral Limit ◽  
Two Fluid

A MODEL HIERARCHY FOR IONOSPHERIC PLASMA MODELING

2004 ◽  
Vol 14 (03) ◽  
pp. 393-415 ◽  
Author(s):  
CHRISTOPHE BESSE ◽  
PIERRE DEGOND ◽  
FABRICE DELUZET ◽  
JEAN CLAUDEL ◽  
GÉRARD GALLICE ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Plasma Density ◽  
Maxwell Equations ◽  
Ionospheric Plasma ◽  
Practical Interest ◽  
Plasma Modeling ◽  
Model Hierarchy ◽  
Great Practical Interest ◽  
Two Fluid ◽  
Insight Into

This paper deals with the modeling of the ionospheric plasma. Starting from the two-fluid Euler–Maxwell equations, we present two hierarchies of models. The MHD hierarchy deals with large plasma density situations while the dynamo hierarchy is adapted to lower density situations. Most of the models encompassed by the dynamo hierarchy are classical ones, but we shall give a unified presentation of them which brings a new insight into their interrelations. By contrast, the MHD hierarchy involves a new (at least to the authors) model, the massless-MHD model. This is a diffusion system for the density and magnetic field which could be of great practical interest. Both hierarchies terminate with the "classical" Striation model, which we shall investigate in detail.

scholarly journals Global Existence and Asymptotic Behavior of Solutions for Compressible Two-Fluid Euler–Maxwell Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-27
Author(s):  
Ismahan Binshati ◽  
Harumi Hattori
Keyword(s):  
Asymptotic Behavior ◽  
Fourier Transform ◽  
Global Existence ◽  
Maxwell Equations ◽  
Decay Rates ◽  
Asymptotic Behavior Of Solutions ◽  
Two Fluids ◽  
The Fourier Transform ◽  
Rates Of Decay ◽  
Two Fluid

We study the global existence and asymptotic behavior of the solutions for two-fluid compressible isentropic Euler–Maxwell equations by the Fourier transform and energy method. We discuss the case when the pressure for two fluids is not identical, and we also add friction between the two fluids. In addition, we discuss the rates of decay of Lp−Lq norms for a linear system. Moreover, we use the result for Lp−Lq estimates to prove the decay rates for the nonlinear systems.

QUASINEUTRAL LIMIT OF THE DRIFT-DIFFUSION MODEL FOR SEMICONDUCTORS WITH GENERAL INITIAL DATA

2003 ◽  
Vol 13 (04) ◽  
pp. 463-470 ◽  
Author(s):  
CHRISTIAN SCHMEISER ◽  
SHU WANG
Keyword(s):  
Initial Data ◽  
Diffusion Model ◽  
Debye Length ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
Uniform Estimates ◽  
Initial Layer ◽  
General Initial Data ◽  
Entropy Functionals ◽  
Quasineutral Limit

The limit for vanishing Debye length (charge neutral limit) in a bipolar drift-diffusion model for semiconductors with general initial data allowing the presence of an initial layer is studied. The quasineutral limit (zero-Debye-length limit) is performed rigorously by using two different entropy functionals which yield appropriate uniform estimates. This investigation extends the results of Refs. 7 and 8 for charge neutral initial data where no initial layer occurs.

scholarly journals Darcy's law and diffusion for a two-fluid Euler–Maxwell system with dissipation

2015 ◽  
Vol 25 (11) ◽  
pp. 2089-2151 ◽  
Author(s):  
Renjun Duan ◽  
Qingqing Liu ◽  
Changjiang Zhu
Keyword(s):  
Magnetic Field ◽  
Initial Data ◽  
Frequency Domain ◽  
Large Time ◽  
Darcy’S Law ◽  
Darcy's Law ◽  
Time Behavior ◽  
Maxwell System ◽  
The Magnetic Field ◽  
Two Fluid

This paper is concerned with the large-time behavior of solutions to the Cauchy problem on the two-fluid Euler–Maxwell system with dissipation when initial data are around a constant equilibrium state. The main goal is the rigorous justification of diffusion phenomena in fluid plasma at the linear level. Precisely, motivated by the classical Darcy's law for the nonconductive fluid, we first give a heuristic derivation of the asymptotic equations of the Euler–Maxwell system in large time. It turns out that both the density and the magnetic field tend time-asymptotically to the diffusion equations with diffusive coefficients explicitly determined by given physical parameters. Then, in terms of the Fourier energy method, we analyze the linear dissipative structure of the system, which implies the almost exponential time-decay property of solutions over the high-frequency domain. The key part of the paper is the spectral analysis of the linearized system, exactly capturing the diffusive feature of solutions over the low-frequency domain. Finally, under some conditions on initial data, we show the convergence of the densities and the magnetic field to the corresponding linear diffusion waves with the rate [Formula: see text] in L2-norm and also the convergence of the velocities and the electric field to the corresponding asymptotic profiles given in the sense of the generalized Darcy's law with the faster rate [Formula: see text] in L2-norm. Thus, this work can be also regarded as the mathematical proof of the Darcy's law in the context of collisional fluid plasma.

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