Constraint-induced restriction and extension operators with applications  

作　　者：陈波 李孝伟 刘高联 

机构地区：[1]Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2009年第11期1345-1352,共8页应用数学和力学（英文版）

基　　金：supported by the National Natural Science Foundation of China (No.10772103);the Shanghai Leading Academic Discipline Project (No.Y0103)

摘　　要：The Stokes operator is a differential-integral operator induced by the Stokes equations. In this paper, we analyze the Stokes operator from the point of view of the Helmholtz minimum dissipation principle. We show that, through the Hodge orthogonal decomposition, a pair of bounded linear operators, a restriction operator and an extension operator, are induced from the divergence-free constraint. As a consequence, we use it to calculate the eigenvalues of the Stokes operator.The Stokes operator is a differential-integral operator induced by the Stokes equations. In this paper, we analyze the Stokes operator from the point of view of the Helmholtz minimum dissipation principle. We show that, through the Hodge orthogonal decomposition, a pair of bounded linear operators, a restriction operator and an extension operator, are induced from the divergence-free constraint. As a consequence, we use it to calculate the eigenvalues of the Stokes operator.

关 键 词：Stokes operator induced operators restriction and extension variationalmethod Hodge decomposition eigenvalue problem 

分 类 号：O177[理学—数学]