白噪声和泊松随机测度驱动的倒向重随机微分方程

本文研究了一类由白噪声和泊松随机测度驱动的倒向重随机微分方程,并建立了此类方程解的定义以及Yamada-Watanabe定理.     

带有指数型非线性项的离散泊松方程和热方程

该文主要利用单调迭代法和比较原理研究了带有指数型非线性项的离散泊松方程和带有指数型非线项的离散热方程解的存在性之间的关系,主要给出了带有指数型非线性项的离散泊松方程解存在时,带有指数型非线项的离散热方程解的渐近稳定性.     

跳扩散模型下股价服从几何布朗运动的Esscher变换定价

考虑跳扩散模型下期权的Esscher变换定价,给出了Esscher变换下带跳的B-S矩生成函数和复合泊松过程下的矩生成函数,推导出跳扩散模型下期权的Esscher变换定价公式.     

基于跳扩散过程的欧式交换期权定价

考虑了股票价格服从带时滞泊松跳的跳扩散模型的欧式交换期权定价问题,运用无套利理论推导出期权价值微分方程,利用变换计价单位的方法,得到交换期权的显示定价公式.     

马尔可夫调制及带Poisson跳随机时滞微分方程依分布稳定

本文讨论马尔可夫调制及带Poisson跳随机时滞微分方程,其主要目的是研究方程解的依分布稳定.     

带跳和右连左极障碍的反射非Lipschitz倒向随机微分方程(英文）

本文考虑一类由布朗运动和泊松点过程驱动的非Lipschitz系数的一维倒向随机微分方程,并要求它的解在一右连左极的障碍过程的上方.利用罚方法和迭代方法证得该类方程解的存在唯一性.     

关于带跳的反射扩散过程的随机最优控制问题

研究一类半空间上带泊松跳的反射扩散过程的随机最优控制问题。得到关于这一控制问题的非线性Nisio半群,和联系这一半群的带Neumann边界条件的哈密顿。雅可比。贝尔曼方程。讨论这一类方程的粘性解的存在唯一性等问题。证明该控制问题中的价值函数是这一方程的一个粘性解。     

多维带跳倒向双重随机微分方程解的性质

本文研究一类多维带跳倒向双重随机微分方程, 给出了It\^{o}公式在带跳倒向双重随机积分情形下的推广形式, 同时运用推广形式的It\^{o}公式, 在Lipschitz条件下证明了方程解的存在性和唯一性.     

带周期位势平面薛定谔-泊松方程组的结点解

利用临界点理论中的亏格定理和Nehari流形技巧,本文证明了在二维全空间上一类带周期位势的薛定谔-泊松方程组高能量解的存在性,且该解存在无穷多个结点区域.更进一步,得到了其基态解的存在性且是不变号的.     

欧式双向期权的两种定价比较

在股票价格服从泊松跳模型下,分别利用保险精算方法与无套利定价方法给出了欧式双向期权的定价公式;通过对这两种结果的比较发现,当股票价格服从特定的泊松跳模型时两种定价公式是相同的.     

On the blow up criterion for the 2-D compressible Navier-Stokes equations

Motivated by [10], we prove that the upper bound of the density function j9 controls the finite time blow up of the classical solutions to the 2-D compressible isentropic Navier-Stokes equations. This result generalizes the corresponding result in [3] concerning the regularities to the weak solutions of the 2-D compressible Navier-Stokes equations in the periodic domain.     

Remarks on nontrivial pullback attractors of the 2-D Navier-Stokes equations with delays

This paper is concerned with some further research on the pullback dynamics for 2-D Navier-Stokes equations with delays. By some new definition of generalized Grashof numbers, we presented some sufficient conditions when the pullback attractors of the 2-D nonautonomous incompressible Navier-Stokes equations with differential continuous delays become a single trajectory, which is a preparation for the fractal dimension of pullback attractors for our problem with constant or variable delays.     

Equations de navier-stokes 3-D avec force de coriolis et viscosité verticale évanescente

We consider the 3-D Navier-Stokes equations with Coriolis force of order 1/z and vanishing vertical viscosity of order ɛ. For suitable initial data, we prove some global or long-time existence results. Moreover, we obtain convergence as ɛ goes to 0 to the 2-D Navier-Stokes equations. We deal with periodic boundary conditions and non-homogeneous strain: in this case, we compute and justify the corrector.     

Remark on the Lifespan of Solutions to 3-D Anisotropic Navier Stokes Equations

The goal of this article is to provide a lower bound for the lifespan of smooth solutions to 3-D anisotropic incompressible Navier-Stokes system,which in particular extends a similar type of result for the classical 3-D incompressible Navier-S tokes system.     

Periodic Structure of 2-D Navier-Stokes Equations

We study in this article both the structure and the structural evolution of the solutions of 2-D Navier-Stokes equations with periodic boundary conditions and the evolution of their solutions. First the structure of all eigenvectors of the corresponding Stokes problem is lassified using a block structure, and is linked to the typical structure of the Taylor vortices. Then the structure of the solutions of the Navier-Stokes equations forced either by eigenmodes or by potential forcing is classified.     

Sharp Estimates for the Number of Degrees of Freedom for the Damped-Driven 2-D Navier-Stokes Equations

We derive upper bounds for the number of asymptotic degrees (determining modes and nodes) of freedom for the two-dimensional Navier-Stokes system and Navier-Stokes system with damping. In the first case we obtain the previously known estimates in an explicit form, which are larger than the fractal dimension of the global attractor. However, for the Navier-Stokes system with damping, our estimates for the number of the determining modes and nodes are comparable to the sharp estimates for the fractal dimension of the global attractor. Our investigation of the damped-driven 2-D Navier-Stokes system is inspired by the Stommel-Charney barotropic model of ocean circulation where the damping represents the Rayleigh friction. We remark that our results equally apply to the viscous Stommel-Charney model.     

Enhanced dissipation for the Kolmogorov flow via the hypocoercivity method Dedicated to Professor Jean-Yves Chemin on the Occasion of His 60th Birthday

In this paper, we solve Beck and Wayne's conjecture on the optimal enhanced dissipation rate for the 2-D linearized Navier-Stokes equations around the bar state called the Kolmogorov flow by developing the hypocoercivity method introduced by Villani(2009).     

Stationary viscous flows at zero surface tension

Stationary solutions of free boundary problems for the Navier-Stokes equations are considered with and without surface tension. The linearized problem in a half-space is studied. Exact solutions of the Poiseuille type are obtained. Properties of the free boundary smoothness in 3-D and 2-D cases are discussed.     

流面上的Navier-Stokes方程及其维数分裂方法

该文首先提出了流面和流层的概念,然后推导出了半测地坐标系下流层内的三维NS (Navier-Stokes)方程,以及流面上的二维NS方程.通过引入流面上的流函数,得到了流函数方程的非线性初边值问题,并讨论了方程解的存在性和唯一性.基于以上讨论,提出了求解三维NS方程的维数分裂方法, 并给出了算例.     

Enhanced dissipation for the Kolmogorov flow via the hypocoercivity method

Science China Mathematics - In this paper, we solve Beck and Wayne’s conjecture on the optimal enhanced dissipation rate for the 2-D linearized Navier-Stokes equations around the bar state...