Navier-Stokes and stochastic Navier-Stokes equations via Lagrange multipliers

拉格朗日乘子与稳态Stokes方程

The Lagrange multiplier and the stationary Stokes equations

本文在希尔伯特空间框架下讨论线性约束的拉格朗日乘子概念，并证明稳态Stokes方程中的压力p正是不可压缩约束div u=0所对应的拉格朗日乘子。

拉格朗日乘子与特征函数

Lagrange multipliers and characteristic functions

本文研究带梯度约束和障碍物的稳态变分不等式，证明其可由含拉格朗日乘子与特征函数的方程刻画，并进一步证明了数据收敛时解的稳定性。

Convergence of a mass conserving Allen-Cahn equation whose Lagrange multiplier is nonlocal and local

We consider the mass conserving Allen-Cahn equation proposed in \cite{Bra-Bre}: the Lagrange multiplier which ensures the conservation of the mass contains not only nonlocal but also local effects (in contrast with \cite{Che-Hil-Log}). As a parameter related to the thickness of a diffuse internal layer tends to zero, we perform formal asymptotic expansions of the solutions. Then, equipped with these approximate solutions, we rigorously prove the convergence to the volume preserving mean curvature flow, under the assumption that classical solutions of the latter exist. This requires a precise a…

Navier-Stokes方程在乘子空间中通过一个速度分量的梯度的正则性准则

A regularity criterion in multiplier spaces to Navier-Stokes equations via the gradient of one velocity component

本文在乘子空间中利用单个速度分量的梯度，建立了三维不可压缩Navier-Stokes方程弱解的正则性准则。

演化向量值变分不等式与拉格朗日乘子

An evolutionary vector-valued variational inequality and Lagrange multiplier

本文证明了受约束向量值函数凸集上演化向量值变分不等式解的存在唯一性，将其转化为含 $L^p$ 拉格朗日乘子的方程组，并证明了给定数据收敛时乘子问题解的收敛性。

梯度流拉格朗日乘子法的唯一可解性与误差分析

Unique solvability and error analysis of the Lagrange multiplier approach for gradient flows

本文针对梯度流的原始拉格朗日乘子法，给出唯一可解性的充分必要条件并提出修正方法，以 Cahn-Hilliard 方程为例证明二阶格式的唯一可解性与最优误差估计，数值实验表明修正方法更鲁棒且允许更大时间步长。