Quasineutral limit of bipolar quantum hydrodynamic model for semiconductors

This paper is concerned with the quasineutral limit of the bipolar quantum hydrodynamic model for semiconductors. It is rigorously proved that the strong solutions of the bipolar quantum hydrodynamic model converge to the strong solution of the so-called quantum hydrodynamic equations as the Debye length goes to zero. Moreover, we obtain the convergence of the strong solutions of bipolar quantum hydrodynamic model to the strong solution of the compressible Euler equations with damping if both the Debye length and the Planck constant go to zero simultaneously.     

Vanishing viscosity and Debye-length limit to rarefaction wave with vacuum for the 1D bipolar Navier–Stokes–Poisson equation

In this paper, we consider the one-dimensional (1D) compressible bipolar Navier–Stokes–Poisson equations. We know that when the viscosity coefficient and Debye length are zero in the compressible bipolar Navier–Stokes–Poisson equations, we have the compressible Euler equations. Under the case that the compressible Euler equations have a rarefaction wave with one-side vacuum state, we can construct a sequence of the approximation solution to the one-dimensional bipolar Navier–Stokes–Poisson equations with well-prepared initial data, which converges to the above rarefaction wave with vacuum as the viscosity and the Debye length tend to zero. Moreover, we also obtain the uniform convergence rate. The results are proved by a scaling argument and elaborate energy estimate.     

Quasineutral limit of the viscous quantum hydrodynamic model for semiconductors

The quasineutral limit (zero-Debye-length limit) of viscous quantum hydrodynamic model for semiconductors is studied in this paper. By introducing new modulated energy functional and using refined energy analysis, it is shown that, for well-prepared initial data, the smooth solution of viscous quantum hydrodynamic model converges to the strong solution of incompressible Navier-Stokes equations as the Debye length goes to zero.     

Quasineutral limit of the pressureless Euler–Poisson equation

In this short paper, we consider the quasineutral limit for the pressureless Euler–Poisson system for ions. By applying the modulated energy method, it shows that the weak solutions for the Euler–Poisson system converge weakly to the strong solutions of the compressible Euler equation as the Debye length tends to zero.     

Quasi-neutral limit of the full bipolar Euler-Poisson system

The quasi-neutral limit of the multi-dimensional non-isentropic bipolar Euler-Poisson system is considered in the present paper. It is shown that for well-prepared initial data the smooth solution of the nonisentropic bipolar Euler-Poisson system converges strongly to the compressible non-isentropic Euler equations as the Debye length goes to zero.     

Quasi-neutral limit for the full Euler–Poisson system in one-dimensional space

In this paper, we consider the quasi-neutral limit of the full Euler–Poisson system in one-dimensional space when the Debye length tends to zero. Due to the observation that the full Euler–Poisson system is Friedrich symmetrizable, we can obtain uniform estimates by applying the pseudo-differential energy estimates. It is shown that for well-prepared initial data the strong solution of the full Euler–Poisson system converges strongly to the compressible Euler equations in small time interval.     

The quasineutral limit of compressible Navier-Stokes-Poisson system with heat conductivity and general initial data

The quasineutral limit of compressible Navier-Stokes-Poisson system with heat conductivity and general (ill-prepared) initial data is rigorously proved in this paper. It is proved that, as the Debye length tends to zero, the solution of the compressible Navier-Stokes-Poisson system converges strongly to the strong solution of the incompressible Navier-Stokes equations plus a term of fast singular oscillating gradient vector fields. Moreover, if the Debye length, the viscosity coefficients and the heat conductivity coefficient independently go to zero, we obtain the incompressible Euler equations. In both cases the convergence rates are obtained.     

The combined quasineutral and low Mach number limit of Euler–Poisson equations coupled to a magnetic field

In this paper, we consider the combined quasineutral and low Mach number limit of compressible Euler–Poisson system coupled to a magnetic field. We prove that, as the Debye length and the Mach number tend to zero simultaneously in some way, the solution of compressible Euler–Poisson system coupled to a magnetic field will converge to that of ideal incompressible magnetohydrodynamic equations with a sharp convergence rate.     

Quasineutral limit of a time-dependent drift-diffusion-Poisson model for p-n junction semiconductor devices

In this paper the vanishing Debye length limit of the bipolar time-dependent drift-diffusion-Poisson equations modelling insulated semiconductor devices with p-n junctions (i.e., with a fixed bipolar background charge) is studied. For sign-changing and smooth doping profile with ‘good’ boundary conditions the quasineutral limit (zero-Debye-length limit) is performed rigorously by using the multiple scaling asymptotic expansions of a singular perturbation analysis and the carefully performed classical energy methods. The key point in the proof is to introduce a ‘density’ transform and two λ-weighted Liapunov-type functionals first, and then to establish the entropy production integration inequality, which yields the uniform estimate with respect to the scaled Debye length. The basic point of the idea involved here is to control strong nonlinear oscillation by the interaction between the entropy and the entropy dissipation.     

Quasineutral limit of a standard drift diffusion model for semiconductors

The limit of vanishing Debye length (charge neutral limit) in a nonlinear bipolar drift-diffusion model for semiconductors without pn-junction (i.e. without a bipolar background charge) is studied. The quasineutral limit (zero-Debye-length limit) is performed rigorously by using the weak compactness argument and the so-called entropy functional which yields appropriate uniform estimates.     

Quasineutral Limit of the Vlasov-Poisson System with Massless Electrons

In this paper, we study the quasineutral limit (in other words the limit when the Debye length tends to zero) of Vlasov-Poisson like equations describing the behavior of ions in a plasma. We consider massless electrons, with a charge density following a Maxwell-Boltzmann law. For cold ions, using the relative entropy method, we derive the classical Isothermal Euler or the (inviscid) Shallow Water systems from fluid mechanics. We then study the combined quasineutral and strong magnetic field regime for such plasmas.     

Quasi-neutral Limit of a Nonlinear Drift Diffusion Model for Semiconductors

The limit of the vanishing Debye length (the charge neutral limit) in a nonlinear bipolar drift-diffusion model for semiconductors without a pn-junction (i.e., with a unipolar background charge) is studied. The quasi-neutral limit (zero-Debye-length limit) is determined rigorously by using the so-called entropy functional which yields appropriate uniform estimates.     

半导体中非线性漂流扩散模型的拟中性极限:快扩散情形

本文研究无Pn-联结的非线性双极半导体漂流扩散模型的消失Debye长度极限(即粒子中性极限)问题．使用熵方法和弱紧性方法从数学上严格证明了快扩散情形的拟中性极限．     

Global convergence of the Euler‐Poisson system for ion dynamics

We consider smooth solutions of the Euler‐Poisson system for ion dynamics in which the electron density is replaced by a Boltzmann relation. The system arises in the modeling of plasmas, where appear two small parameters, the relaxation time and the Debye length. When the initial data are sufficiently close to constant equilibrium states, we prove the convergence of the system for all time, as each of the parameters goes to zero. The limit systems are drift‐diffusion equations and compressible Euler equations. The proof is based on uniform energy estimates and compactness arguments.     

Quasineutral limit of an euler-poisson system arising from plasma physics

In this paper, we study the quasineutral limit of an Euler-Poisson system arising from plasma physics i.e. the limit when the Debye length tends to of a non linear hyperbolic system coupled with a non linear elliptic equation.The proof uses pseudodiiferential energy estimates techniques, in order to justify classical limits in small time, for strong solutions.     

Some limit analysis of a three dimensional viscous compressible capillary model for plasma

In this study, we discuss some limit analysis of a viscous capillary model of plasma, which is expressed as a so‐called the compressible Navier‐Stokes‐Poisson‐Korteweg equation. First, the existence of global smooth solutions for the initial value problem to the compressible Navier‐Stokes‐Poisson‐Korteweg equation with a given Debye length λ and a given capillary coefficient κ is obtained. We also show the uniform estimates of global smooth solutions with respect to the Debye length λ and the capillary coefficient κ. Then, from Aubin lemma, we show that the unique smooth solution of the 3‐dimensional Navier‐Stokes‐Poisson‐Korteweg equations converges globally in time to the strong solution of the corresponding limit equations, as λ tends to zero, κ tends to zero, and λ and κ simultaneously tend to zero. Moreover, we also give the convergence rates of these limits for any given positive time one by one.     

Singularity formation to the 2D Cauchy problem of nonbarotropic magnetohydrodynamic equations without heat conductivity

The question of whether the two-dimensional (2D) nonbarotropic compressible magnetohydrodynamic (MHD) equations with zero heat conduction can develop a finite-time singularity from smooth initial data is a challenging open problem in fluid dynamics and mathematics. Such a problem is interesting in studying global well-posedness of solutions. In this paper, we proved that, for the initial density allowing vacuum states, the strong solution exists globally if the density and the pressure are bounded from above. Our method relies on weighted energy estimates and a Hardy-type inequality.     

On the stability of contact discontinuity for Cauchy problem of compress Navier-Stokes equations with general initial data

In this paper,we study the stability of solutions of the Cauchy problem for 1-D compressible NarvierStokes equations with general initial data.The asymptotic limit of solution is found,under some conditions.The results in this paper imply the case that the limit function of solution as t →∞ is a viscous contact wave in the sense,which approximates the contact discontinuity on any finite-time interval as the heat conduction coefficients toward zero.As a by-product,the decay rates of the solution for the fast diffusion equations are also obtained.The proofs are based on the elementary energy method and the study of asymptotic behavior of the solution to the fast diffusion equation.     

Low Mach number limit of global solutions to 3‐D compressible nematic liquid crystal flows with Dirichlet boundary condition

In this paper, we consider the uniform estimates of strong solutions in the Mach number ? and t ∈ [0,∞) for the compressible nematic liquid crystal flows in a 3‐D bounded domain , provided the initial data are small enough and the density is close to the constant state. Here, we consider the case that the velocity field satisfies the Dirichlet boundary condition. Based on the uniform estimates, we obtain the global convergence of the compressible nematic liquid crystal system to the incompressible nematic liquid crystals system as the Mach number tends to zero.     

Quasi-neutral limit to the drift-diffusion models for semiconductors with physical contact-insulating boundary conditions

In this paper the limit of vanishing Debye length in a bipolar drift-diffusion model for semiconductors with physical contact-insulating boundary conditions is studied in one-dimensional case. The quasi-neutral limit (zero-Debye-length limit) is proved by using the asymptotic expansion methods of singular perturbation theory and the classical energy methods. Our results imply that one kind of the new and interesting phenomena in semiconductor physics occurs.