Analysis for symmetric and non-decaying viscous incompressible flows
| Project/Area Number |
15H06312
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Mathematical analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
Abe Ken 京都大学, スーパーグローバルコース数学系ユニット, 特定助教 (80748327)
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| Project Period (FY) |
2015-08-28 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | ナヴィエ・ストークス方程式 / 有界関数空間 / ストークス半群 / 解析半群 / 軸対称解 / 外部問題 / 非減衰初期値 / 流体 / 軸対称流 / 非減衰流 |
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| Outline of Final Research Achievements |
I have studied regularity and asymptotic behavior of solutions for the Navier-Stokes equations, which describes the motion of viscous incompressible flows such as the atmosphere and the water. In this research project, I have worked on the two problems.
The first problem is an axisymmetric solution. I have constructed global unique axisymmetric solutions in an exterior domain subject to the slip boundary condition for decaying and sufficiently smooth initial data.
The second is a non-decaying solution. I have constructed local-in-time unique solutions in an exterior domain in a space of bounded functions. For the two-dimensional case, I have proved that global unique solutions exist for bounded initial data with a finite Dirichlet integral.
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Report
(3 results)
Research Products
(30 results)
