| Project/Area Number |
24654032
|
|---|
| Research Category |
Grant-in-Aid for Challenging Exploratory Research
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Waseda University |
|---|
Principal Investigator |
KOZONO Hideo 早稲田大学, 理工学術院, 教授 (00195728)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
KANEDA Yukio 愛知工業大学, 工学部, 教授 (10107691)
|
|---|
| Project Period (FY) |
2012-04-01 – 2015-03-31
|
| Project Status |
Completed (Fiscal Year 2014)
|
| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
|---|
| Keywords | Navier-Stokes 方程式 / 外部問題の弱解の一意性 / 領域の位相幾何と可解性 / エネルギー不等式 / 指数安定性 / 非斉次境界値問題 / 流量条件 / 大きな解の安定性 / Leray-Fujita の不等式 / Dirichelt積分 / 物体を通り過ぎる流れ / 回転流体 / Dirichlet積分 / 弱解の一意性 |
|---|
| Outline of Final Research Achievements |
To the 3D stationary Navier-Stokes equations in exterior domains, if the obstacle rotates slowly around the axis and moves also slowly along the same direction to the axis, then there exists a unique strong solution. In particular, we investigate the case when the obstacle moves with a constant speed and succeed to prove the energy inequality for any weak solution provided the external force is in the dual space of homogeneous Sobolev space with the first derivative in L^2. As an application, we can show the uniqueness of weak solutions under the smallness assumption on external forces. On the other hand, in the interior domain with multi-connected boundaries, if the inhomogeneous boundary data satisfies the Leray-Fujita inequality and if the stationary weak solution is close to the extended solenoidal vector field in L^3-norm, then it is asymptotically stable with an exponential convergence rate.
|
