Mathematical analysis of fluid-structure interaction
| Project/Area Number |
15K04954
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical analysis
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| Research Institution | Nagoya University |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 非圧縮粘性流 / Navier-Stokes方程式 / 発展作用素 / Oseen流 / 外部問題 / 漸近展開 / 制御 / 長時間挙動 / 安定性 / 漸近挙動 / Stokes半群 / Oseen半群 / 最適制御 / Stokes流 / 減衰構造 |
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| Outline of Final Research Achievements |
I analyzed a problem arising from fluid-structure interaction and some related issues, where the fluid is incompressible as well as viscous, while the structure is assumed to be a rigid body. In 3D case the boundary controllability of a self-propelled motion of a body, whose motion is prescribed but not too large, was proved. Toward analysis of this solution, I deduced a large time behavior of the evolution operator generated by a linearized system around time-dependent rigid motions. A new result on the starting problem in 3D proposed by Finn was also provided. In 2D case an asymptotic representation of steady flows at spatial infinity around a rotating body was discovered. I also deduced a temporal decay estimate of the Oseen semigroup past a translating body in 2D.
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| Academic Significance and Societal Importance of the Research Achievements |
非圧縮粘性流と物体の運動の相互作用の問題、また物体の運動がその周りの流れに与える効果の解析は、未解明な事柄が多く、古くて新しい問題である。問題意識は数学の中で閉じておらず、流体物理学や流体工学においても重要な位置を占めるが、本研究によって、数学的な基礎をある段階まで与えることができたことは意義深い。特に、上記の成果の一つである境界での制御可能性について、制御関数は例えば水中を泳ぐ微生物の繊毛による駆動を表し、与えられた運動を達成するために繊毛をどのように使えばよいかに答えている。抵抗最小な最適制御解の安定性を調べるには、本研究で得られた発展作用素の時間減衰評価の応用が有効であると期待される。
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Report
(5 results)
Research Products
(44 results)
