The 3D Non-isentropic Compressible Euler Equations with Damping in a Bounded Domain

The authors investigate the global existence and asymptotic behavior of classical solutions to the 3D non-isentropic compressible Euler equations with damping on a bounded domain with slip boundary condition. The global existence and uniqueness of classical solutions are obtained when the initial data are near an equilibrium. Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.     

Initial layers and zero‐relaxation limits of multidimensional Euler–Poisson equations

In this paper, we consider zero‐relaxation limits for periodic smooth solutions of the time‐dependent Euler–Poisson system. For well‐prepared initial data, we construct an approximate solution by an asymptotic expansion up to any order. For ill‐prepared initial data, we construct initial layer corrections in an explicit way. In both cases, the asymptotic expansions are valid in a time interval independent of the relaxation time, and their convergence is justified by establishing uniform energy estimates. Copyright © 2012 John Wiley & Sons, Ltd.     

Initial layers and zero-relaxation limits of Euler–Maxwell equations

In this paper we consider zero-relaxation limits for periodic smooth solutions of Euler–Maxwell systems. For well-prepared initial data, we propose an approximate solution based on a new asymptotic expansion up to any order. For ill-prepared initial data, we construct initial layer corrections in an explicit way. In both cases, the asymptotic expansions are valid in time intervals independent of the relaxation time and their convergence is justified by establishing uniform energy estimates.     

The non-relativistic limit of Euler–Maxwell equations for two-fluid plasma

This paper is concerned with two-fluid time-dependent non-isentropic Euler–Maxwell equations in a torus for plasmas or semiconductors. By using the method of formal asymptotic expansions, we analyze the non-relativistic limit for periodic problems with the prepared initial data. It is shown that the small parameter problems have unique solutions existing in the finite time interval where the corresponding limit problems (compressible Euler–Poisson equations) have smooth solutions. Moreover, the formal limit is rigorously justified by an iterative scheme and an analysis of asymptotic expansions up to any order.     

非线性扰动Klein-Gordon方程初值问题的渐近理论

在二维空间中研究一类非线性扰动Klein-Gordon方程初值问题解的渐近理论. 首先利用压缩映象原理,结合一些先验估计式及Bessel函数的收敛性,根据Klein-Gordon方程初值问题的等价积分方程,在二次连续可微空间中得到了初值问题解的适定性;其次,利用扰动方法构造了初值问题的形式近似解,并得到了该形式近似解的渐近合理性;最后给出了所得渐近理论的一个应用,用渐近近似定理分析了一个具体的非线性Klein-Gordon方程初值问题解的渐近近似程度．     

Rigorous derivation of incompressible type Euler equations from non-isentropic Euler-Maxwell equations

In this paper, we investigate the convergence of the time-dependent and non-isentropic Euler-Maxwell equations to incompressible Euler equations in a torus via the combined quasi-neutral and non-relativistic limit. For well prepared initial data, the convergences of solutions of the former to the solutions of the latter are justified rigorously by an analysis of asymptotic expansions and energy method.     

On the Asymptotic Representation of a Regularization Approach to Nonlinear Semiexplicit Higher-Index Differential-Algebraic Equations

Differential-algebraic equations with a higher index can beapproximated by regularization algorithms. One such possibilitywas introduced by März for linear time-varying index 2systems and extended by the author to index 3 systems. In thepresent paper, März’s approach is generalized tononlinear semiexplicit index 2 and 3 equations. The structureof the regularized solutions and their convergence propertiesare characterized in terms of asymptotic expansions.     

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.     

Zero Dissipation Limit to Rarefaction Waves for the 1-D Compressible Navier-Stokes Equations

The zero dissipation limit for the one-dimensional Navier-Stokes equations of compressible,isentropic gases in the case that the corresponding Euler equations have rarefaction wave solutions is investi...     

关于一类非线性微分方程组的边值问题的渐近解（Ⅰ）

应用新的方法 ,研究一类非线性微分方程组　　u″ =v,εv″ f(x ,u ,u′)v′ -g(x ,u ,u′)v =0　　 (0 <ε 1) ,的边值问题的解的渐近性质·　构造出解的渐近展开式 ,和估计了余项 ,改进并拓广了前人的工作·     

关于一类带有慢变系数的二阶微分方程的渐近解

本文研究一类带有慢变系数的二阶常微分方程解的渐近展开式.指出已有工作的不足,利用改进的多重尺度法改进和拓广了文献[1～4]的结果.     

可压缩的Navier—Stokes方程H^2强解的整体存在性

该文对于三维可压缩的Navier-Stokes方程，当其具有小扰动初值时，证明了H2（R3）强解的整体存在性．     

Global Solution of an Initial-Value Problem for Two-Dimensional Compressible Euler Equations

This paper is concerned with the existence of global continuous solutions of the expansion of a wedge of gas into a vacuum for compressible Euler equations. By hodograph transformation, we first prove that the flow is governed by a partial differential equation of second order, which is further reduced to a system of two nonhomogeneous linearly degenerate equations in the phase space under an irrotationality condition. Then this conclusion is applied to solving the problem that a wedge of gas expands into a vacuum, which is actually a Goursat-type problem for these two equations in the supersonic domain.     

Asymptotic Analysis of Steady and Nonsteady Navier-Stokes Equations for Barotropic Compressible Flow

We study the asymptotic behavior of solutions to steady and nonsteady Navier-Stokes equations for barotropic compressible fluids with slip boundary conditions in small channels whose diameters converge to zero. We also derive the corresponding asymptotic one-dimensional equations and we analyze the sets, where L ¹-weak convergence of the pressure terms fails.     

Convergent Expansions for Solutions of Linear Ordinary Differential Equations Having a Simple Turning Point, with an Application to Bessel Functions

Second-order linear ordinary differential equations with a large parameter u are examined. Classic asymptotic expansions involving Airy functions are applicable for the case where the argument z lies in complex domain containing a simple turning point. In this article, such asymptotic expansions are converted into convergent series, where u appears in an inverse factorial, rather than an inverse power. The domain of convergence of the new expansions is rigorously established and is found to be an unbounded domain containing the turning point. The theory is then applied to obtain convergent expansions for Bessel functions of complex argument and large positive order.     

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。     

Asymptotic Solutions of Hamilton-Jacobi Equations with State Constraints

We study Hamilton-Jacobi equations in a bounded domain with the state constraint boundary condition. We establish a general convergence result for viscosity solutions of the Cauchy problem for Hamilton-Jacobi equations with the state constraint boundary condition to asymptotic solutions as time goes to infinity.     

关于Boussinesq方程组无粘极限的研究

该文主要研究三维Boussinesq方程组的无粘极限问题.为了克服Boussinesq方程组中温度和速度耦合项产生的困难,带温度的涡量方程需要与Slip边界条件匹配,通过计算得到温度更高阶的边界条件,结合迹定理和能量估计,最后得到了三维粘性Boussinesq方程组初边值问题强解的存在唯一性,并在平坦区域上得到了强解的收敛率.     

Global Existence and Asymptotic Behavior for the 3D Compressible Non–isentropic Euler Equations with Damping

We investigate the global existence and asymptotic behavior of classical solutions for the 3D compressible non-isentropic damped Euler equations on a periodic domain. The global existence and uniqueness of classical solutions are obtained when the initial data is near an equilibrium. Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.