| Project/Area Number |
18K03363
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Review Section |
Basic Section 12020:Mathematical analysis-related
|
|---|
| Research Institution | Nagoya University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2018-04-01 – 2024-03-31
|
| Project Status |
Completed (Fiscal Year 2023)
|
| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2020: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2018: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
|
|---|
| Keywords | 非圧縮粘性流 / Navier-Stokes方程式 / fluid-structure / 安定性 / self-propelled運動 / 最適制御 / 発展作用素 / 漸近挙動 / Fluid-structure / 外部問題 / 時間周期解 / 長時間挙動 / 制御 / 漸近展開 / Navier-Stokes |
|---|
| Outline of Final Research Achievements |
I studied several aspects of fluid-structure interaction and related problems. The fluid flows obey the Navier-Stokes system in the exterior of a rigid body, whereas the motions of the body are governed by conservation of linear and angular momentum. A stability criterion for nontrivial basic motions auch as steady and periodic solutions was deduced in the case of a rigid ball. The result is new even for steady motions, and analysis developed here allows us to discuss the stability of time-dependent motions. As for steady fluid-structure interaction with rigid bodies of arbitrary shape, optimal control at the boundary was studied within the self-propelled regime. I also established the large time behavior of the evolution operator arising from time-dependent rigid motions. As applications, existence, spatial pointwise behavior and attainability of time-periodic solutions were proved. Finally, the asymptotic structure of steady motions affected by rotation of the body was clarified.
|
| 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、特に剛体の運動の制御と安定性、また関連して剛体の運動がその周りの流れに与える効果の解析は、数学的に難しい構造をもつために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、それらに支えられる応用科学において重要な位置を占めるが、本研究によって数学的な基礎を一定な水準まで与えることができたことは意義深い。特に、主流が時間依存であるときの安定性は久しく未解決であったが、その周りでの線型化非自励系が生成する発展作用素の時間減衰評価は解決へ向けて決定的な役割を果たし、またその解析手法自体も汎用性が高い。
|
