纵向数据下半参数回归模型的统计分析

对于纵向数据下半参数回归模型,基于广义估计方程和一般权函数方法构造了模型中参数分量和非参数分量的估计.在适当的条件下证明了参数估计量具有渐近正态性,并得到了非参数回归函数估计量的最优收敛速度.通过模拟研究说明了所提出的估计量在有限样本下的精确性.     

黎曼流形上薛定谔方程的Harnack估计

推导了薛定谔方程正解的一种新的整体梯度估计和Harnack不等式,推广了一些有关热方程的结论,并且得到了一个关于薛定谔算子的刘维尔定理.     

Laplace方程斜边值问题的梯度估计

该文介绍了Laplace方程斜边值问题解的梯度估计的两种证明方法:第一种证明重新整理文献[1]中的梯度估计;第二种证明采用不同于文献[1]的辅助函数得到估计.两种方法都充分利用函数在极大值点的性质,得到边界梯度估计和近边梯度估计,结合文献[2]中已有的梯度内估计,从而得到解的全局梯度估计.     

乘子空间中广义Navier-Stokes方程弱解的正则性准则(英文)

利用能量估计与不等式研究三维广义Navier-Stokes方程弱解的正则性准则,证明如果速度场的水平分量ū=(u1,u2,0)满足ū∈L2α-(r+1)2α(0,T;r),r∈[0,1),或者水平速度场的水平梯度▽hū=(α1ū,α2ū)满足▽hū∈L2α-r2α(0,T;r),r∈[0,1],则弱解在[0,T)是唯一的强解.     

《流体自然对流换热中的数值方法》研究概述

<正> 其中μ为粘性系数,p为压力,c_p为定压比热,(g_x,g_y,,g_z)为g的x、y、z方向的分量. 若考察竖直环形空腔内流体自然对流换热问题,选取圆柱坐标系,将z轴取得与重力g方向相同,那么,连续性方程、动量方程、能量方程表示如下     

一种非线性抛物方程在一般几何流下的梯度估计（英文）

本文通过Li-Yau梯度估计的方法和Jun Sun对热方程在一般几何流下梯度估计的研究,推导出一类重要的非线性抛物方程在一般几何流演化下的梯度估计,并得到了哈拿克不等式等一些结论.推广了Wang的结果.     

黎曼流形上一类非线性抛物方程的梯度估计（英文）

本文得到了黎曼流形上一类非线性抛物方程的局部Hamilton梯度估计.利用这个局部梯度估计,得到了一个Harnack型不等式.     

非线性抛物型方程的全离散有限元方法

§1.引言关于非线性抛物型方程有限元方法的研究已有许多工作.但所讨论的方程关于梯度是线性的,仅得到全离散有限元逼近的L_2误差估计及较弱意义下(两层平均)的H~1误差估计.本文讨论关于梯度亦是非线性的抛物型方程.得到了最佳L_2、H~1(较强意义下)、L.及时间导数的误差估计. 考虑下述抛物型方程的混合问题:     

非线性Kirchhoff型波动方程全局吸引子的存在性

非线性Kirchhoff型波动方程描述了竖直方向上的波动.利用近似FaedoGalerkin的方法通过先验估计和一种新的验证紧性的方法(条件C)讨论了这类波动方程强解的全局吸引子.     

Riemann流形上改进的p-Laplace方程的梯度估计

本文研究Riemann流形上的改进的p-Laplace方程,运用截断函数的估计、Hessian比较定理和Laplace比较定理,得到该方程正解的梯度估计.并应用该结论,得到在Riemann流形上关于改进的p-Laplace方程正解的Harnack不等式和Liouville型定理.     

Self-similar Solutions of the Navier–Stokes Equations on Weak Weighted Lorentz Spaces

In the present paper, we prove the existence of global solutions for the Navier–Stokes equations in Rnwhen the initial velocity belongs to the weighted weak Lorentz space Λn,∞(u) with a sufficiently small norm under certain restriction on the weight u. At the same time, self-similar solutions are induced if the initial velocity is, besides, a homogeneous function of degree-1. Also the uniqueness is discussed.     

Global strong solutions to 3-D Navier-Stokes system with strong dissipation in one direction Dedicated to Professor Jean-Yves Chemin on the Occasion of His 60th Birthday

We consider three-dimensional incompressible Navier-Stokes equations(NS) with different viscous coefficients in the vertical and horizontal variables. In particular, when one of these viscous coefficients is large enough compared with the initial data, we prove the global well-posedness of this system. In fact, we obtain the existence of a global strong solution to(NS) when the initial data verifies an anisotropic smallness condition which takes into account the different roles of the horizontal and vertical viscosity.     

On the global null controllability of a Navier-Stokes system with Navier slip boundary conditions

In this paper, we deal with a two-dimensional Navier-Stokes system in a rectangle with Navier slip boundary conditions on the horizontal sides. We establish the global null controllability of the system by controlling the normal component and the vorticity of the velocity on the vertical sides. The linearized control system around zero is controllable but one does not know how to deduce global controllability results for the nonlinear system. Our proof uses the return method together with a local exact controllability result by Fursikov and Imanuvilov.     

The Inviscid Initial Value Problem for a Piecewise Linear Mean Flow

The time evolution of a small disturbance on a piecewise linear mean flow, approximating a parabolic profile, is calculated using Fourier transform methods. The solution is found to consist of two parts: one dispersive, incorporating the spreading of waves; one convective, characterized by a convection of the disturbance with the local mean velocity. Two dispersive modes are found: one symmetric with respect to the channel center line and one antisymmetric. The dispersivity of the symmetric mode is in fair agreement with the symmetric mode obtained for inviscid parabolic flow, whereas the antisymmetric mode is misrepresented. One of the parts of the solution to the horizontal velocities is found to be purely three-dimensional. This results from fluid elements retaining part of their horizontal momentum as they are lifted up by the time integrated effect of the vertical velocity. Calculations of the development of a particular disturbance modeling two vortex pairs are also made. The results show that the dispersive part, although decaying, is largest for the vertical velocity. For the horizontal velocity the three-dimensional lift-up effect provides the largest amplitudes. This part does not show any sign of decay, in agreement with earlier analysis by Gustavsson [8] and Landahl [16]. This last effect partly explains the sensitivity to three-dimensional disturbances seen in transition experiments and calculations. Comparison of the solution to a full numerical simulation using the Navier-Stokes equations shows good agreement for short times.     

Global strong solutions to 3-D Navier-Stokes system with strong dissipation in one direction

Science China Mathematics - We consider three-dimensional incompressible Navier-Stokes equations (NS) with different viscous coefficients in the vertical and horizontal variables. In particular,...     

Vanishing viscosity limit for a coupled Navier-Stokes/Allen-Cahn system

In this paper, we study the vanishing viscosity limit for a coupled Navier-Stokes/Allen-Cahn system in a bounded domain. We first show the local existence of smooth solutions of the Euler/Allen-Cahn equations by modified Galerkin method. Then using the boundary layer function to deal with the mismatch of the boundary conditions between Navier-Stokes and Euler equations, and assuming that the energy dissipation for Navier-Stokes equation in the boundary layer goes to zero as the viscosity tends to zero, we prove that the solutions of the Navier-Stokes/Allen-Cahn system converge to that of the Euler/Allen-Cahn system in a proper small time interval. In addition, for strong solutions of the Navier-Stokes/Allen-Cahn system in 2D, the convergence rate is cν1/2.     

A Liouville Theorem for the Planer Navier-Stokes Equations with the No-Slip Boundary Condition and Its Application to a Geometric Regularity Criterion

We establish a Liouville type result for a backward global solution to the Navier-Stokes equations in the half plane with the no-slip boundary condition. No assumptions on spatial decay for the vorticity nor the velocity field are imposed. We study the vorticity equations instead of the original Navier-Stokes equations. As an application, we extend the geometric regularity criterion for the Navier-Stokes equations in the three-dimensional half space under the no-slip boundary condition.     

Existence of global weak solutions for Navier-Stokes equations with large flux

Global existence of weak solutions to the Navier-Stokes equations in a cylindrical domain under boundary slip conditions and with inflow and outflow is proved. To prove the energy estimate, crucial for the proof, we use the Hopf function. This makes it possible to derive an estimate such that the inflow and outflow need not vanish as t→∞. The proof requires estimates in weighted Sobolev spaces for solutions to the Poisson equation. Our result is the first step towards proving the existence of global regular special solutions to the Navier-Stokes equations with inflow and outflow.     

Solvability of the Navier-Stokes equations on manifolds with boundary

This paper deals with the solvability of the Navier-Stokes equations on manifolds with boundary. In particular, we concentrate on the inhomogeneous slip boundary condition. Our formulation of the equations takes into account a curvature term which results from a proper derivation of the Navier-Stokes equations. This term has not been considered in prior work. During the work on this version, the author received technical support through a fellowship of the DFG     

Regularity for the Navier-Stokes equations with slip boundary condition

For the Navier-Stokes equations with slip boundary conditions, we obtain the pressure in terms of the velocity. Based on the representation, we consider the relationship in the sense of regularity between the Navier-Stokes equations in the whole space and those in the half space with slip boundary data.