约束诱导的限制和扩张算子及其应用  

Constraint Induced Restriction and Extension Operators With Applications

作　　者：陈波[1] 李孝伟[1] 刘高联[1] 

机构地区：[1]上海大学,上海市应用数学和力学研究所,上海200072

出　　处：《应用数学和力学》2009年第11期1261-1267,共7页Applied Mathematics and Mechanics

基　　金：上海市重点学科建设资助项目(Y0103);国家自然科学基金资助项目(10772103)

摘　　要：Stokes方程是由动量方程和不可压缩约束耦合而成的方程组,Stokes算子是由Stokes方程诱导所得到的微分-积分算子.该文试从Helmholtz最小耗散原理的角度,采用对零散度矢量场进行Hodge正交分解的方法,对Stokes算子的性质进行分析.结果指出Stokes算子是Helmholtz耗散泛函的Frchet导算子,零散度约束通过Hodge正交分解诱导出一对有界线性算子,即限制算子R和扩张算子ε.作为结果的应用,利用它计算Stokes算子的特征值.The Stokes operator is a differential-integral operator induced by the Stokes equations. From the point of view of the Helmholtz minimum dissipation principle the Stokes operator was analyzed. It＇ s shown that, through the Hodge orthogonal decomposition, a pair of bounded linear operators, namely, a restriction operator and an extension operator, are induced from the divergence-free constraint. As a consequence of the observation,it＇ s utilized to calcu late the eigenvalues of the Stokes operator.

关 键 词：STOKES算子 诱导算子 HODGE分解 变分方法 特征值问题 

分 类 号：O357.1[理学—流体力学]