Convergence of the nonisentropic Euler-Poisson equations to incompressible type Euler equations

In this paper, we investigate a multidimensional nonisentropic hydrodynamic (Euler-Poisson) model for semiconductors. We study the convergence of the nonisentropic Euler-Poisson equation to the incompressible nonisentropic Euler type equation via the quasi-neutral limit. The local existence of smooth solutions to the limit equations is proved by an iterative scheme. The method of asymptotic expansion and energy methods are used to rigorously justify the convergence of the limit.     

Classical solutions to relativistic Burgers equations in FLRW space-times

We are interested in the classical solutions to the Cauchy problem of relativistic Burgers equations evolving in Friedmann-Lemat?tre-Robertson-Walker(FLRW)space-times,which are spatially homogeneous,isotropic expanding or contracting universes.In such kind of space-times,we first derive the relativistic Burgers equations from the relativistic Euler equations by letting the pressure be zero.Then we can show the global existence of the classical solution to the derived equation in the accelerated expanding space-times with small initial data by the method of characteristics when the spacial dimension n=1 and the energy estimate when n 2,respectively.Furthermore,we can also show the lifespan of the classical solution by similar methods when the expansion rate of the space-times is not so fast.     

Smooth solutions for one‐dimensional relativistic radiation hydrodynamic equations

In this research article, we investigated the existence of local smooth solutions for relativistic radiation hydrodynamic equations in one spatial variable. The proof is based on a classical iteration method and the Banach contraction mapping principle. However, because of the complexity of relativistic radiation hydrodynamics equations, we first rewrite this system into a semilinear form to construct the iteration scheme and then use left eigenvectors to decouple the system instead of applying standard energy method on symmetric hyperbolic systems. Different from multidimensional case, we just use the characteristic method, which can keep the properties of the initial data. Copyright © 2015 John Wiley & Sons, Ltd.     

Characteristic decompositions and boundary value problems for two‐dimensional steady relativistic Euler equations

In this paper, we investigate Goursat problems, and mixed initial and boundary value problems for the two‐dimensional steady relativistic Euler equations. The global existence of classical solutions to these problems are obtained by using the characteristic decomposition method. Some applications of these results in supersonic flow in two‐dimensional ducts and the two‐dimensional relativistic jet are discussed. Copyright © 2013 John Wiley & Sons, Ltd.     

Multiple stationary solutions of euler-poisson equations for non-isentropic gaseous stars

The motion of the self-gravitational gaseous stars can be described by the Euler-Poisson equations. The main purpose of this paper is concerned with the existence of stationary solutions of Euler-Poisson equations for some velocity fields and entropy functions that solve the conservation of mass and energy. Under different restriction to the strength of velocity field, we get the existence and multiplicity of the stationary solutions of Euler-Poisson system.     

On the Steady State Relativistic Euler-Poisson Equations

We are concerned with the mathematical analysis of the relativistic Euler-Poisson equations in one dimensional case. The existence and uniqueness of the related smooth steady state solutions are proved. The non-relativistic limit and zero-relaxation limit of the model as well as their convergence rates are also obtained.     

GLOBAL EXISTENCE AND EXPONENTIAL STABILITY OF SMOOTH SOLUTIONS TO A MULTIDIMENSIONAL NONISENTROPIC EULER-POISSON EQUATIONS

The global existence and large time behavior of smooth solutions to multi-dimensional nonisentropic Euler-Poisson equations are established.     

Convergence of Compressible Euler-Maxwell Equations to Compressible Euler-Poisson Equations

In this paper,the convergence of time-dependent Euler-Maxwell equations to compressible Euler-Poisson equations in a torus via the non-relativistic limit is studied. The local existence of smooth solutions to both systems is proved by using energy esti- mates for first order symmetrizable hyperbolic systems.For well prepared initial data the convergence of solutions is rigorously justified by an analysis of asymptotic expansions up to any order.The authors perform also an initial layer analysis for general initial data and prove the convergence of asymptotic expansions up to first order.     

Stabilities for Euler-Poisson equations in some special dimensions

We study the stabilities and classical solutions of Euler-Poisson equations describing the evolution of the gaseous star in astrophysics. In fact, we extend the study of the stabilities of Euler-Poisson equations with or without frictional damping term to some special dimensional spaces. Besides, by using the second inertia function in 2 dimension of Euler-Poisson equations, we prove the non-global existence of classical solutions with , for any γ.     

有限初始能量的相对论欧拉方程组光滑解的爆破

在初始资料的某些限制下证明有限初始能量的相对论欧拉方程组柯西问题光滑解的爆破.该文的爆破条件不需要初始资料具有紧支集,部分补充了Pan和Smoller的经典爆破结果(2006).     

Asymptotic Behavior of Global Smooth Solotions to the Euler-Poisson System in Semiconductors

In this paper, we establish the global existence and the asymptotic behavior of smooth solution to the initial-boundary value problem of Euler-Poisson system which is used as the bipolar hydrodynamic model for semiconductors with the nonnegative constant doping profile.     

A global solution curve for a class of periodic problems,including the relativistic pendulum

Using continuation methods, we study the global solution structure of periodic solutions for a class of periodically forced equations, generalizing the case of relativistic pendulum. We obtain results on the existence and multiplicity of periodic solutions. Our approach is suitable for numerical computations, and in fact we present some numerically computed bifurcation diagrams illustrating our results.     

Local Smooth Solutions to the 3-Dimensional Isentropic Relativistic Euler equations

The authors consider the local smooth solutions to the isentropic relativistic Euler equations in （3＋1）-dimensional space-time for both non-vacuum and vacuum cases. The local existence is proved by symmetrizing the system and applying the Friedrichs- Lax-Kato theory of symmetric hyperbolic systems. For the non-vacuum case, according to Godunov, firstly a strictly convex entropy function is solved out, then a suitable sym- metrizer to symmetrize the system is constructed. For the vacuum case, since the coefficient matrix blows-up near the vacuum, the authors use another symmetrization which is based on the generalized Riemann invariants and the normalized velocity.     

Existence of global smooth solution to the relativistic Euler equations

In this paper, we prove an existence theorem of global smooth solutions to the Cauchy problem for the one-dimensional relativistic Euler equations. The analysis is based on a priori estimates which are obtained by the characteristic method and maximum principle.     

带自由边界的可压缩欧拉与欧拉-泊松方程组径向对称解的爆破北大核心CSCD

本文在R^(N)(N=2,3)中研究描述流向外部真空的可压缩流体的欧拉与欧拉-泊松方程组径向对称解的爆破.在分离流体与真空的连续自由边界条件下考虑其自由边值问题.对于径向对称的欧拉方程组,证明若初始流平均向外流动,则其光滑解将在有限时刻爆破.对于带有斥力与弛豫项的单极与双极径向对称欧拉-泊松方程组,证明若某个与初始动量有关的加权泛函适当大,则其光滑解将在有限时刻爆破。     

Generalized Electrodynamics With Ternary Internal Structure

In Refs. [2]–[7] we suggested generalized dynamic equations of motion of relativistic charged particles inside electromagnetic fields. The dynamic equations had been formulated in terms of external as well as internal momenta. Evolution equations for external momenta, the Lorentz-force equations, had been derived from evolution equations for internal momenta. In this paper, along with relativistic dynamics we generalize electromagnetic fields within the scope of ternary algebras. The full theory is constructed in 4D euclidean space. This space possesses an advantage to build ternary mappings from three vectors onto one. The dynamics is given by non-linear evolution equations with cubic characteristic polynomial. In polar representation the internal momenta obey the Jacobi equations whereas external momenta obey the Weierstrass equations for elliptic functions. The generalized electromagnetic fields are defined by the triple fields where the first one has properties of the electric field and the other two have properties of the magnetic field. The field equations for the triple fields analogous to the Maxwell equations are suggested.     

等离子体中带小参数的高维流体动力学双极模型的渐近展开(英文)

通过渐近展开的方法,研究了等离子体中带小参数的双极Euler-Poisson方程的拟中性极限和零松弛时间极限问题.对于每一个极限,只要具有好准备的初值,就可以得到任意阶渐近展开的存在唯一性,并在最后讨论了这些极限的验证问题.     

Global existence and asymptotic behavior of solutions to the nonisentropic bipolar hydrodynamic models

In this paper, we consider a one-dimensional bipolar nonisentropic hydrodynamical model from semiconductor devices. This system takes the nonisentropic Euler-Poisson form with electric field and frictional damping added to the momentum equations. First, we prove global existence of smooth solutions to the Cauchy problem. Next, we also discuss the asymptotic behavior of the smooth solutions. We find that in large time, the densities of electron and hole tend to the same nonlinear diffusive wave, the momentums tend to the Darcy's law, and the temperatures tend to the ambient device temperature. Finally, we can obtain the algebraic decay rate of the densities to the same nonlinear diffusive wave, the momentums to the Darcy's law and the temperatures to the ambient device temperature, and the exponential decay of their difference and the electric field to zero. We can show our results by precise energy methods.     

Relaxation-time limit of the multidimensional bipolar hydrodynamic model in Besov space

In this paper, we study a multidimensional bipolar hydrodynamic model for semiconductors or plasmas. This system takes the form of the bipolar Euler-Poisson model with electric field and frictional damping added to the momentum equations. In the framework of the Besov space theory, we establish the global existence of smooth solutions for Cauchy problems when the initial data are sufficiently close to the constant equilibrium. Next, based on the special structure of the nonlinear system, we also show the uniform estimate of solutions with respect to the relaxation time by the high- and low-frequency decomposition methods. Finally we discuss the relaxation-time limit by compact arguments. That is, it is shown that the scaled classical solution strongly converges towards that of the corresponding bipolar drift-diffusion model, as the relaxation time tends to zero.     

Global convergence of an isentropic Euler-Poisson system in $\R^+ \times \R^d$

We prove the global-in-time convergence of an Euler-Poisson system near a constant equilibrium state in the whole space $\R^d$, as physical parameters tend to zero. The result follows from the uniform global existence of smooth solutions by means of energy estimates together with compactness arguments. For this purpose, we establish uniform estimates for $\dive \,u$ and $\curle \,u$ instead of $\nabla u$.