2012 Fiscal Year Final Research Report
Analysis of nonlinear partial differential equations with nonlocal property
| Project/Area Number |
21740092
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Osaka University |
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Principal Investigator |
MIURA Hideyuki 大阪大学, 大学院・理学研究科, 助教 (20431497)
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| Project Period (FY) |
2009 – 2012
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| Keywords | 分数拡散方程式 / 楕円型境界値問題 / 特異点除去可能性 / 外部問題 / Navier-Stokes方程式 / 渦度方向 / Landau 解 |
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| Research Abstract |
In this project, we considered nonlinear partial differential equations with nonlocal property. We obtained some results on the regularity and the asymptotic behavior of the incompressible Navier-Stokes flows and the property of the fundamental solutions for certain fractional diffusion equations. Besides these results, we introduced some methods for the analysis of the nonlocal partial differential equations. We expect these methods can be applied for future research.
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