2010 Fiscal Year Final Research Report
Mathematical analysis of motions of bodies in a viscous fluid
| Project/Area Number |
19540170
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Nagoya University (2008-2010)
Niigata University (2007) |
|---|
Principal Investigator |
HISHIDA Toshiaki Nagoya University, 多元数理科学研究科, 教授 (60257243)
|
|---|
| Project Period (FY) |
2007 – 2010
|
| Keywords | 非圧縮粘性流体 / Navier-Stokes方程式 / Stokes方程式 / 外部領域 / 漸近挙動 |
|---|
| Research Abstract |
Suppose that there is an obstacle, which is a rigid body, in a viscous incompressible fluid. Toward analysis of body-fluid interaction, let us consider the Navier-Stokes flow in the exterior of the body when it is rotating with constant angular velocity. We first proved the existence and stability of the steady flow in 3D and derived the large time behavior of a unique global solution around that steady flow. The similar results were obtained for the time-periodic flow as well. We next deduced the decay structure and asymptotic profile of the steady flow at space infinity. The decay structure of the steady flow in 2D was also provided, so that we found the resolution of the Stokes paradox by the rotation of the body.
|
Research Products
(19 results)
