可压缩核废料污染问题的修正迎风差分格式及收敛性分析

对无弥散项的可压缩核废料污染问题模型建立修正迎风差分格式,并进行了收敛性分 析,最后给出其l2误差估计．     

不可压流体的边界层问题

研究三维有界区域在边界上有流动的不可压流体的边界层问题,导出了Navier-Stokes方程区域内部的近似方程(Euler方程和线性化的Euler方程)和边界附近近似的方程(零阶边界层方程与一阶边界层方程),证明了这种近似的合理性.     

GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR FOR AN 1-D COMPRESSIBLE ENERGY TRANSPORT MODEL

In this article, the global existence and the large time behavior of smooth solutions to the initial boundary value problem for a degenerate compressible energy transport model are established.     

一维非等温可压缩Navier-Stokes-Korteweg方程组稀疏波的整体稳定性（英文）

可压缩Navier-Stokes-Korteweg方程组可用来描述具有内部毛细作用的粘性可压缩流体的运动.本文研究了毛细系数依赖于密度、粘性系数和热传导系数依赖于温度的一维非等温的可压缩Navier-Stokes-Korteweg方程组Cauchy问题解的大时间行为.利用基本的L~2能量方法,我们证明如果相应的Euler方程组的黎曼问题存在稀疏波解,那么所考虑的一维可压缩Navier-Stokes-Korteweg方程组存在唯一的整体强解,并且当时间趋于无穷大时,此强解趋向于稀疏波.这里初始扰动和稀疏波的强度都可以任意大.     

Weak Dissipative Structure for Compressible Navier-Stokes Equations

This paper concerns the Cauchy problem for compressible Navier-Stokes equations.The weak dissipative structure is explored and a new proof for the classical solutions are shown to exist globally in time if the initial data is sufficiently small.     

Strong （Weak） Exact Controllability and Strong （Weak） Exact Observability for Quasilinear Hyperbolic Systems

Numerical approximations of Cahn-Hilliard phase-field model for the two-phase incompressible flows are considered in this paper.Several efficient and energy stable time discretization schemes for the coupled nonlinear Cahn-Hilliard phase-field system for both the matched density case and the variable density case are constructed,and are shown to satisfy discrete energy laws which are analogous to the continuous energy laws.     

Examples of boundary layers associated with the incompressible Navier-Stokes equations

The author surveys a few examples of boundary layers for which the Prandtl boundary layer theory can be rigorously validated. All of them are associated with the incompressible Navier-Stokes equations for Newtonian fluids equipped with various Dirichlet boundary conditions (specified velocity). These examples include a family of (nonlinear 3D) plane parallel flows, a family of (nonlinear) parallel pipe flows, as well as flows with uniform injection and suction at the boundary. We also identify a key ingredient in establishing the validity of the Prandtl type theory, i.e., a spectral constraint on the approximate solution to the Navier-Stokes system constructed by combining the inviscid solution and the solution to the Prandtl type system. This is an additional difficulty besides the wellknown issue related to the well-posedness of the Prandtl type system. It seems that the main obstruction to the verification of the spectral constraint condition is the possible separation of boundary layers. A common theme of these examples is the inhibition of separation of boundary layers either via suppressing the velocity normal to the boundary or by injection and suction at the boundary so that the spectral constraint can be verified. A meta theorem is then presented which covers all the cases considered here.     

具有奇性与真空粘性依赖于密度的非牛顿流局部强解的存在唯一性

研究一维有界区间上粘性依赖于密度且具有奇性、初始允许真空的可压缩非牛顿流.通过正则化奇性项以及逐步迭代构造初边值问题的逼近解,对逼近解取极限得到其局部强解的存在唯一性,进一步推广了相关文献中关于非牛顿流解的存在性结果.     

可压缩流体力学高精度拉格朗日格式及其保正性质

本文对可压缩流体力学高精度拉格朗日格式及其保正性质近年来的发展给出回顾与综述.文中分别介绍了一维、二维可压缩流体力学方程中心型拉格朗日格式的设计步骤,回顾了高精度拉格朗日格式以及高精度保正拉格朗日格式的研究进展.     

三维不可压缩黏弹性流体系统解的逐点估计

本文考虑三维不可压缩黏弹性流体力学模型的Cauchy问题.首先引入适当的变量变换,对变换后的方程组,研究其线性化系统的Green函数.接着,根据Green函数逐点估计方法,结合方程组解的表达式,分析Riesz算子的影响,得到解关于时空的逐点估计.