一维粘性液体-气体两相流模型自由边值问题全局强解存在唯一性

本文建立了一类粘性两相流模型,主要研究了当初始密度间断连接到真空时的全局强解存在唯—性.利用一系列的先验估计得到m和n的正上下界估计;再运用差分方法,证明了可压缩粘性液体-气体两相流模型的全局强解存在唯—性,这样我们把Evje,Karlsen和姚磊,朱长江的结论推广到β＞0,γ＞max{β+1,2β}的情形.     

半导体磁流体动力学模型经典解的整体适定性

研究一类半导体磁流体动力学模型,它是由关于电子的质量和速度的守恒律方程耦合Maxwell方程构成的流体动力学方程组.在小初值条件下,运用经典的双曲能量方法,得到了磁流体动力学模型Cauchy问题经典解的整体适定性.     

Global Strong Solutions for the Viscous,Micropolar, Compressible Flow

In this paper, we consider the viscous, micropolar, compressible flow in one dimension. We give the proof of existence and uniqueness of strong solutions for the initial boundary problem that vacuum can be allowed initially.     

Global Well-Posedness of Classical Solutions with Large Initial Data to the Two-Dimensional Isentropic Compressible Navier-Stokes Equations

We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the two-dimensional isentropic compressible Navier-Stokes equations with smooth initial data under the assumption that the viscosity coefficient μ is large enough. Here we do not require that the initial data is small.     

Boussinesq方程温和解的全局适定性北大核心CSCD

Boussinesq方程作为描述许多地球物理现象的模型,是Navier-Stokes方程与热力学方程之间耦合的零阶近似.利用隐函数定理,研究带黏性高维Boussinesq系统,并得到了小初值位于尺度不变空间时温和解的全局适定性.     

Global Existence of Large Data Weak Solutions for a Simplified Compressible Oldroyd-B Model Without Stress Diffusion

We start with the compressible Oldroyd-B model derived in [2] (J. W. Barrett, Y. Lu, and E. Süli, Existence of large-data finite-energy global weak solutions to a compressible Oldroyd-B model, Commun. Math. Sci., 15 (2017), 1265-1323), where the existence of global-in-time finite-energy weak solutions was shown in two dimensional setting with stress diffusion. In the paper, we investigate the case without stress diffusion. We first restrict ourselves to the corotational setting as in [28] (P. L. Lions, and N. Masmoudi, Global solutions for some Oldroyd models of non-Newtonian flows, Chin. Ann. Math., Ser. B, 21(2) (2000), 131-146). We further assume the extra stress tensor is a scalar matrix and we derive a simplified model which takes a similar form as the multi-component compressible Navier-Stokes equations, where, however, the pressure term related to the scalar extra stress tensor has the opposite sign. By employing the techniques developed in [30,35], we can still prove the global-in-time existence of finite energy weak solutions in two or three dimensions, without the presence of stress diffusion.     

Strong Solutions for Nonhomogeneous Incompressible Viscous Heat-Conductive Fluids with Non-Newtonian Potential

We consider the Navier-Stokes system with non-Newtonian potential for heat-conducting incompressible fluids in a domain Ω R3. The viscosity, heat conduc- tion coefficients and specific heat at constant volume are allowed to depend smoothly on the density and temperature. We prove the existence of unique local strong solu- tions for all initial data satisfying a natural compatibility condition. The difficult of this type model is mainly that the equations are coupled with elliptic, parabolic and hyper- bolic, and the vacuum of density cause also much trouble, that is, the initial density need not be positive and may vanish in an open set.     

广义强向量拟平衡问题解的存在性和Hadamard适定性

首先,在映射－f(·,y,u)自然拟C-凸和映射f上半(－C)-连续的条件下,构造一个重要辅助函数,利用不同的证明方法,在不要求C*具有弱*紧基的情况下,建立了广义强向量拟平衡问题解的存在性定理.然后在适当条件下,给出问题序列收敛的定义,建立解集映射的上半连续性,并讨论广义强向量拟平衡问题的Hadamard适定性,得到广义强向量拟平衡问题的Hadamard适定性成立的充分条件.     

六阶对流Cahn-Hilliard方程解的整体适定性

In this paper,we consider the global well-posedness of smooth solutions for the Cauchy problem of a sixth order convective Cahn-Hilliard equation with small initial data.We first construct a local smooth solution,then by combining some a priori estimates,continuity argument,the local smooth solution is extended step by step to all t>0 provided that the L1 norm of initial data is suitably small and the smooth nonlinear functions f(u)and g(u)satisfy certain local growth conditions at some fixed point■.     

一类强交错扩散的捕食模型弱解的整体存在性

考虑一类带有强交错扩散项的捕食模型解的整体存在性.借助于有限差分方法和熵不等式的相关性质及结论,证明了在高维空间上,该问题有整体存在的弱解.此外,还说明了所得的这个弱解是非负解.     

Global Existence of Large BV Solutions in a Model of Granular Flow

In this paper we analyze a set of equations proposed by Hadeler and Kuttler [20 Hadeler , K. P. , Kuttler , C. ( 1999 ). Dynamical models for granular matter . Granular Matter 2 : 9 – 18 . [Google Scholar]], describing the flow of granular matter in terms of the heights of a standing layer and of a moving layer. By a suitable change of variables, the system can be written as a 2 × 2 hyperbolic system of balance laws, which we study in the one-dimensional case. The system is linearly degenerate along two straight lines in the phase plane, and therefore is weakly linearly degenerate at the point of the intersection. The source term is quadratic, consisting of product of two quantities, which are transported with strictly different speeds. Assuming that the initial height of the moving layer is sufficiently small, we prove the global existence of entropy-weak solutions to the Cauchy problem, for a class of initial data with bounded but possibly large total variation.     

Global Solutions of Nonlinear Magnetohydrodynamics with Large Initial Data

A free boundary problem for nonlinear magnetohydrodynamics with general large initial data is investigated. The existence, uniqueness, and regularity of global solutions are established with large initial data in H¹. It is shown that neither shock waves nor vacuum and concentration in the solutions are developed in a finite time, although there is a complex interaction between the hydrodynamic and magnetodynamic effects. An existence theorem of global solutions with large discontinuous initial data is also established.     

Strong Solutions to Non-stationary Channel Flows of Heat-Conducting Viscous Incompressible Fluids with Dissipative Heating

We study an initial-boundary-value problem for time-dependent flows of heat-conducting viscous incompressible fluids in channel-like domains on a time interval (0,T). For the parabolic system with strong nonlinearities and including the artificial (the so called “do nothing”) boundary conditions, we prove the local in time existence, global uniqueness and smoothness of the solution on a time interval (0,T ^∗), where 0<T ^∗≤T.     

Global Well-Posedness of the BCL System with Viscosity

The BCL system, a kind of equations governing the motion of the free surface of water waves in R3, is studied. Some results on the global existence, uniqueness and regularity of solutions to such system with small initial data are obtained.     

Global Well-Posedness for Cubic NLS with Nonlinear Damping

We study the Cauchy problem for the cubic nonlinear Schrödinger equation, perturbed by (higher order) dissipative nonlinearities. We prove global in-time existence of solutions for general initial data in the energy space. In particular we treat the energy-critical case of a quintic dissipation in three space dimensions.     

一类广义层流方程初值问题的整体适定性

讨论了刻画层流问题中比重相近的层间相互作用的数学模型的初值问题.通过引进一类函数空间并证明该初值问题的解在所述空间上的一系列先验估计,得到了该初值问题在初值属于Hs(R)(s≥1)时的整体适定性.     

具强吸引项的非线性反应扩散方程的解的全局熄灭问题

设ｆ定义在［０，＋∞）上的非负值连续凹函数并满足．本文证明了对于这类函数ｆ而言，反应扩散方程ｕｔ＝△ｕ－ｆ（ｕ）的初值问题和具有齐次边值条件的初边值问题的解将在有限时刻全局熄灭，并给出了全局熄灭的时间估计．     

Global Existence of Strong Solutions for the Generalized Navier-Stokes Equations with Damping

Acta Mathematicae Applicatae Sinica, English Series - This paper mainly focus on the global existence of the strong solutions for the generalized Navier-Stokes equations with damping. We obtain the...     

一类带有非牛顿位势的可压缩Navier-Stokes方程整体强解的存在性

主要研究了一类带有非牛顿位势的可压缩Navier-Stokes方程:其中粘性系数μ依赖于密度ρ,Φ是非牛顿位势.证明了上述问题的强解的存在性.在相容性条件下,得到了强解的唯一性.