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Navier-Stokes Equations in a Curved Thin Domain, Part I : Uniform Estimates for the Stokes Operator
http://hdl.handle.net/2261/0002007544
http://hdl.handle.net/2261/0002007544f7ef6e63-9b55-4ee1-b73e-ddd7140ca873
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
jms290201.pdf (613.5 KB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||||
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| 公開日 | 2023-05-31 | |||||||
| タイトル | ||||||||
| タイトル | Navier-Stokes Equations in a Curved Thin Domain, Part I : Uniform Estimates for the Stokes Operator | |||||||
| 言語 | en | |||||||
| 言語 | ||||||||
| 言語 | eng | |||||||
| キーワード | ||||||||
| 言語 | en | |||||||
| 主題Scheme | Other | |||||||
| 主題 | Stokes operator | |||||||
| キーワード | ||||||||
| 言語 | en | |||||||
| 主題Scheme | Other | |||||||
| 主題 | curved thin domain | |||||||
| キーワード | ||||||||
| 言語 | en | |||||||
| 主題Scheme | Other | |||||||
| 主題 | slip boundary conditions | |||||||
| キーワード | ||||||||
| 言語 | en | |||||||
| 主題Scheme | Other | |||||||
| 主題 | uniform Korn inequality | |||||||
| キーワード | ||||||||
| 言語 | en | |||||||
| 主題Scheme | Other | |||||||
| 主題 | uniform a priori estimate | |||||||
| 資源タイプ | ||||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||
| 資源タイプ | departmental bulletin paper | |||||||
| 著者 |
Miura, Tatsu-Hiko
× Miura, Tatsu-Hiko
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| 著者所属 | ||||||||
| 言語 | en | |||||||
| 値 | Department of Mathematics, Kyoto university | |||||||
| 抄録 | ||||||||
| 内容記述タイプ | Abstract | |||||||
| 内容記述 | In the series of this paper and the forthcoming papers [47, 48] we study the Navier–Stokes equations in a three-dimensional curved thin domain around a given closed surface under Navier’s slip boundary conditions. We focus on the study of the Stokes operator for the curved thin domain in this paper. The uniform norm equivalence for the Stokes operator and a uniform difference estimate for the Stokes and Laplace operators are established in which constants are independent of the thickness of the curved thin domain. To prove these results we show a uniform Korn inequality and a uniform a priori estimate for the vector Laplace operator on the curved thin domain based on a careful analysis of vector fields and surface quantities on the boundary. We also present examples of curved thin domains and vector fields for which the uniform Korn inequality is not valid but a standard Korn inequality holds with a constant that blows up as the thickness of a thin domain tends to zero. | |||||||
| 言語 | en | |||||||
| 書誌情報 |
en : Journal of Mathematical Sciences The University of Tokyo 巻 29, 号 2, p. 149-256, 発行日 2022-05-27 |
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| ISSN | ||||||||
| 収録物識別子タイプ | ISSN | |||||||
| 収録物識別子 | 13405705 | |||||||
| 書誌レコードID | ||||||||
| 収録物識別子タイプ | NCID | |||||||
| 収録物識別子 | AA11021653 | |||||||
| Mathmatical Subject Classification | ||||||||
| 言語 | en | |||||||
| 値 | 76D07(MSC2010) | |||||||
| Mathmatical Subject Classification | ||||||||
| 言語 | en | |||||||
| 値 | 35Q30(MSC2010) | |||||||
| Mathmatical Subject Classification | ||||||||
| 言語 | en | |||||||
| 値 | 76D05(MSC2010) | |||||||
| Mathmatical Subject Classification | ||||||||
| 言語 | en | |||||||
| 値 | 76A20(MSC2010) | |||||||
| 出版者 | ||||||||
| 出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||||
| 言語 | en | |||||||
| 原稿受領日 | ||||||||
| 値 | 2021-03-04 | |||||||
