三维可压缩Euler方程球对称解的生命区间

对于可压缩的三维Ｅｕｌｅｒ方程，当其初值为振幅ε的小扰动且具有球对称性质时，我们研究了经典解的生命区间．并证明无论初值的扰动多么小，经典解都在有限时间内爆破．     

一个包含欧拉函数的方程

设n为任意正整数,如果n〉1,设n=p1^α1p2^α2…pk^αk是n的标准分解式,函数Ω（n）定义为Ω（1）=0,Ω（n）=∑i=1^kαi,φ（n）为Euler函数,本文的主要目的是利用初等方法研究方程φ（φ（n））=2Ω（n）的可解性,并获得该方程的所有正整数解,从而彻底解决了前学者提出的一个问题．     

三维无界区域上弱阻尼非线性Schrodinger方程的指数吸引子

文［１］中证明了弱阻尼非线性Ｓｃｈｒｄｉｎｇｅｒ方程在无界区域ＲＮ（Ｎ≤３）上存在一个最大的紧吸引子．本文在此基础上得到了Ｒ３上指数吸引子的存在性     

带非线性阻尼项的三维可压缩欧拉方程组的整体解

研究了三维空间中带非线性阻尼项的可压缩欧拉方程组的初值问题.利用能量估计和傅立叶分析的方法,在初值是常状态附近的一个H~3∩L~1中的小扰动时获得了初值问题的解整体存在,并得到了解在大时间的L~2,L~∞衰减率分别为t~(-3/4),t~(-3/2),将线性阻尼的情形推广到了非线性阻尼的情形.     

拟线性椭圆型欧拉方程在无界区域上的非平凡解

本文目的是在 W_0~(12)(Ω)中给出拟线性方程(1)和它的齐次 Dirich- 的非平凡解的存在性证明。这里Ω是 R~N(N≥3)中的满足一定条件的无界区域。     

三维具弱阻尼Schrǒdinger-Boussinesq方程组的周期解

In this paper the authors consider a model of the interaction of a nonlinear complex Schrdinger field and a real Boussinesq field in a 3D domain with the weakly damping which arises in the laser and plasma physics and prove the existence of the periodic solution.     

关于不可压缩的Euler方程的一类解

对于不可压缩的Euler方程，当其初值具有的形式时，本文证明了解的存在性和正则性．     

一类带有快扩散项的半导体方程的弱解存在性

In this paper, we consider the transient drift-diffusion model with fast diffusion term. This problem is not only degenerate but also singular. We present the existence result for the Neumann boundary value problem with general nonlinear diffusivities.     

三维无界区域上耗散Klein-Gordon-Schrodinger方程的指数吸引子

文 ［１］证明了耗散Ｋｌｅｉｎ－Ｇｏｒｄｏｎ－Ｓｃｈｒｏｄｉｎｇｅｒ方程在Ｘ（Ｒ~３）中具有一个最大吸引子,本文在文 ［１］的基础上得到了该方程在Ｘ（Ｒ~３）中拥有一个指数吸引子．     

二维可压缩Euler方程轴对称解的生命区间的下界

对于二维可压缩的Ｅｕｌｅｒ方程，当其初值满足ρ｜ｔ＝０＝ρ，ｄｉｖｖ｜ｔ＝０＝０，ｒｏｔｖ｜ｔ＝０＝εω１００时（０＜ε１），证明了对充分小的ε，存在常数ｂ＞０，使得其经典解的生命区间Ｔεｂｌｎ｜ｌｎε｜ε２．与文［５］中ｌｉｍε０＋ε２Ｔε＝＋∞的结论相比，本文的结果更为精确．     

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.     

Long Time Behavior of Solutions to the 3D Compressible Euler Equations with Damping

Abstract

The effect of damping on the large-time behavior of solutions to the Cauchy problem for the three-dimensional compressible Euler equations is studied. It is proved that damping prevents the development of singularities in small amplitude classical solutions, using an equivalent reformulation of the Cauchy problem to obtain effective energy estimates. The full solution relaxes in the maximum norm to the constant background state at a rate of t ^?(3/2). While the fluid vorticity decays to zero exponentially fast in time, the full solution does not decay exponentially. Formation of singularities is also exhibited for large data.     

三维空间中带非线性阻尼项的等熵欧拉方程组轴对称解的爆破

研究了三维空间中带非线性阻尼项的可压缩等熵欧拉方程组Dirichlet初边值问题.采用泛函方法,定义几种不同的泛函,当初始速度足够大时分别得到了经典解在某一时间内必定爆破的结论.由于出现了非线性阻尼项,较之线性阻尼的情形,经典解爆破的难度随之增加.     

Controllability of the 3D Compressible Euler System

The paper is devoted to the controllability problem for 3D compressible Euler system. The control is a finite-dimensional external force acting only on the velocity equation. We show that the velocity and density of the fluid are simultaneously controllable. In particular, the system is approximately controllable and exactly controllable in projections.     

二维等熵可压欧拉方程古典解的存在性(英文)

研究二维等熵可压缩欧拉方程的古典解存在性.利用迭代技巧,得到解的局部存在性及唯一性,并且还证明了解在有限时间内爆破,即可压缩欧拉方程不存在全局古典解.     

一维可压缩Euler方程组的两个模型

作者考察了一维可压缩Euler方程组的两个模型.利用特征分解和Gronwall不等式,首先得到具有几何结构且绝热指数γ=3的一维可压缩Euler方程组L~∞模的一致有界性.进一步,考虑当绝热指数γ=-1时,一维非等熵可压缩Euler方程组的Cauchy问题.在适当的假设下,得到该系统的整体经典解.     

The 3D compressible Euler equations with damping in a bounded domain

We proved global existence and uniqueness of classical solutions to the initial boundary value problem for the 3D damped compressible Euler equations on bounded domain with slip boundary condition when the initial data is near its equilibrium. Time asymptotically, the density is conjectured to satisfy the porous medium equation and the momentum obeys to the classical Darcy's law. Based on energy estimate, we showed that the classical solution converges to steady state exponentially fast in time. We also proved that the same is true for the related initial boundary value problem of porous medium equation and thus justified the validity of Darcy's law in large time.     

三维可压Euler方程简单波及双重波结构

本文研究了三维可压欧拉方程简单波解和双重波解的结构.给出了简单波的流动区域是被一族相互独立的平面所覆盖,沿着每个平面u,v,w从而p,ρ,c均为常数.双重波的流动区域是被一族相互独立的直线所覆盖,沿着每个特征平面u,v,w从而p,ρ,c均为常数.