2020 Fiscal Year Final Research Report
Mathematical analysis of fluid dynamics in various singular limits
| Project/Area Number |
17K05320
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Mathematical analysis
|
|---|
| Research Institution | Kyoto University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2017-04-01 – 2021-03-31
|
| Keywords | 偏微分方程式 / 流体力学 / Navier-Stokes方程式 / 特異極限問題 / Prandtl境界層展開 / 2次元外部領域Oseen流 |
|---|
| Outline of Final Research Achievements |
In this research some singular perturbation problems arising from the mathematical fluid mechanics are mathematically studied. In particular, the structure of the flow near the boundary, such as the boundary layer for the flow in the high Reynolds number, and its stability are rigorously analyzed. As the main results, this research has revealed the structure of the two-dimensional flow around the rapidly-rotating infinite cylinder, and has established the Prandtl boundary layer expansion around the monotone and concave boundary layer in a suitable functional setting. The asymptotic stability of the two-dimensional Oseen flow is also proved for the small Reynolds number.
|
| Free Research Field |
偏微分方程式
|
| Academic Significance and Societal Importance of the Research Achievements |
レイノルズ数と呼ばれる無次元量が大きな流れは，身近な流体運動においても頻繁に表れ，その特質を数学的に理解することは重要な課題である．これらの問題は，数学的にはNavier-Stokes方程式の特異極限問題として定式化されるが，Navier-Stokes方程式の非線形性と非局所性により，その厳密な解析には大きな困難を伴うことが知られている．本研究成果は，それらの困難を克服する解析手法の確立に大きな貢献を果たすものである．また，動く物体周りの流れとして最も基本的な2次元Oseen定常流の安定性を数学的に示した．この問題は半世紀近く未解決の問題であり，大きな学術的意義を持つ．
|
