| Project/Area Number |
14540171
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Shizuoka University |
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Principal Investigator |
SHIMIZU Senjo Shizuoka University, Faculty of Engineering, Associate professor, 工学部, 助教授 (50273165)
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| Co-Investigator(Kenkyū-buntansha) |
SHIBATA Yoshihiro Waseda University, School of Science and Engineering, Professor, 理工学部, 教授 (50114088)
KIKUCHI Koji Shizuoka University, Faculty of Engineering, Professor, 工学部, 教授 (50195202)
HOSHIGA Akira Shizuoka University, Faculty of Engineering, Associate professor, 工学部, 助教授 (60261400)
ADACHI Shinji Shizuoka University, Faculty of Engineering, Associate professor, 工学部, 助教授 (40339685)
NAKAJIMA Toru Shizuoka University, Faculty of Engineering, Associate professor, 工学部, 助教授 (50362182)
久保 英夫 静岡大学, 工学部, 助教授 (50283346)
太田 雅人 埼玉大学, 理学部, 助教授 (00291394)
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| Project Period (FY) |
2002 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2004: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2003: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2002: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | Stokes Equations / Neumann boundary condition / Resolvent problems / L_p estimates / Analytic semigroups / L_p-L_q estimates / Free boundary problems / Local energy decay / 最大正則性 / 自由境界値問題 / 有界領域 / 外部領域 / 界面問題 / L_p評価 / 非有界領域 |
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| Research Abstract |
In this research, we consider the Stokes equation with Neumann boundary condition which is obtained as a linearized equation of the free boundary problem for the Navier-Stokes equation. We analyzed this problem by the following procedure : (1) Analysis of the resolvent problem (2) Generation of Analytic semigroups (3) L_p-L_q estimates
(1)Obtained is the L_p estimate of solutions to the resolvent problem for Stokes system with Neumann type boundary condition in a bounded or exterior domain in R^n. The result has been obtained by Grubb and Solonnikov by the systematic use of theory of pseudo-differential operators. In this paper, we give an essentially different proof from theirs. The core of my approach is to estimate the solutions in the whole space and half-space case. We apply the Fourier multiplier theorem to solution of the model problems.
(2)First we introduce the Helmholtz decomposition. Then we delete pressure trem and reduce to the problem only including velocity vector. Then we generated analytic semigroup to this reduced Stokes equation.
(3)We obtained local energy decay estimates and L_p-L_q estimates of the solutions to the Stokes equation with Neumann boudary condition. Comparing with the non-slip (Dirichlet) boundary condition case, we have a better decay estimate for the gradient of the semigroup because of the null net force at the boundary.
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