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The Stokes operator with Robin boundary conditions in solenoidal subspaces of L 1(R n +) and L ∞(R n +)
| Title: | The Stokes operator with Robin boundary conditions in solenoidal subspaces of L 1(R n +) and L ∞(R n +) |
| Authors: | Saal, Juergen Browse this author |
| Issue Date: | 2004 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 638 |
| Start Page: | 2 |
| End Page: | 27 |
| Abstract: | We prove that the Stokes operator with Robin boundary conditions is the generator of a bounded holomorphic semigroup on L^\infty_\sigma({\mathbb R}^n_+), which is even strongly continuous on the space \BUC_\sigma({\mathbb R}^n_+). Contrary to that result it is also proved that there exists no Stokes semigroup on L^1_\sigma({\mathbb R}^n_+), except if we assume the special case of Neumann boundary conditions. Nevertheless, we also obtain gradient estimates for the solution of the Stokes equations in L^1_\sigma({\mathbb R}^n_+) for all types of Robin boundary conditions. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69445 |
| 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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