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On isomorphism for the space of solenoidal vector fields and its application to the Stokes problem
| Title: | On isomorphism for the space of solenoidal vector fields and its application to the Stokes problem |
| Authors: | Maekawa, Yasunori Browse this author | | Miura, Hideyuki Browse this author |
| Keywords: | Solenoidal vector fields | | incompressible flows | | Helmholtz projection | | reduction argument | | factorization of elliptic operators |
| Issue Date: | 27-Aug-2015 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1076 |
| Start Page: | 1 |
| End Page: | 15 |
| Abstract: | 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, under suitable functional setting, the space of solenoidal vector fields is isomorphic to the n − 1 product space of the space of scalar functions. As an application, we introduce a natural and 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. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69880 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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