中文摘要：

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Fr6chet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，即限制算子勇和扩张算子ε．作为结果的应用，利用它计算Stokes算子的特征值．

英文摘要：

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.