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The Stokes operator with Robin boundary conditions in solenoidal subspaces of L 1(R n +) and L ∞(R n +)

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83791

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
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

Submitter: 数学紀要登録作業用

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