2018年
On isomorphism for the space of solenoidal vector fields and its application to the incompressible flows
SIAM Journal on Mathematical Analysis
- ,
- 巻
- 50
- 号
- 1
- 開始ページ
- 339
- 終了ページ
- 353
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1137/16M1093537
- 出版者・発行元
- Society for Industrial and Applied Mathematics Publications
We consider the space of solenoidal vector fields in an unbounded domain Ω ⊂ Rn whose boundary is given as a Lipschitz graph. It is shown that the space of solenoidal vector fields is isomorphic to the n − 1 product space of the space of scalar functions in some natural topology such as L2(Ω). As an application, we introduce a systematic reduction of the equations describing the motion of incompressible flows. This gives a new perspective of the derivation of Ukai’s solution formula for the Stokes equations in the half space and provides a key step for the generalization of Ukai’s approach to the Stokes semigroup in the case of the curved boundary.
- リンク情報
- ID情報
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- DOI : 10.1137/16M1093537
- ISSN : 1095-7154
- ISSN : 0036-1410
- SCOPUS ID : 85043538936