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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Stokes operator ： ウィキペディア英語版 Stokes operator The Stokes operator, named after George Gabriel Stokes, is an unbounded linear operator used in the theory of partial differential equations, specifically in the fields of fluid dynamics and electromagnetics. ==Definition== If we define $P\_\backslash sigma$ as the Leray-Helmholtz projector onto divergence free vector fields, then the Stokes Operator $A$ is defined by :$A:=-P\_\backslash sigma\backslash triangle,$ where $\backslash triangle\backslash equiv\backslash nabla^2$ is the Laplacian. Since $A$ is unbounded, we must also give its domain of definition, which is defined as $\backslash mathcal(A)=H^2\backslash cap\; V$, where $V=\backslash \backslash ,\backslash vec=0\backslash \}$. Here, $\backslash Omega$ is a bounded open set in $\backslash mathbb^n$ (usually ''n'' = 2 or 3), $H^2(\backslash Omega)$ and $H^1\_0(\backslash Omega)$ are the standard Sobolev spaces, and the divergence of $\backslash vec$ is taken in the distribution sense. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Stokes operator」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.