2009 Fiscal Year Final Research Report
Mathematical analysis of nonlinear partial differential equations related with vorticity fields of viscous incompressible flows
| Project/Area Number |
20840033
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| Research Category |
Grant-in-Aid for Young Scientists (Start-up)
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Kyushu University |
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Principal Investigator |
MAEKAWA Yasunori Kyushu University, 大学院・理学研究科, 講師 (70507954)
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| Project Period (FY) |
2008 – 2009
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| Keywords | 偏微分方程式 / 流体力学 / 非圧縮性粘性流体 / Navier-Stokes方程式 / 渦度方程式 / Burgers渦 / 安定性解析 |
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| Research Abstract |
It is well-known that vorticity fields play important roles in dynamics of incompressible flows. This research aims to analyze linear and nonlinear partial differential equations related with vorticity fields mathematically. As one of the results obtained in this research, it is rigorously proved that some stationary solutions which are known as a model of a coherent structure of vortex tubes in turbulent flows are asymptotically stable with respect to small three-dimensional perturbation flows. This research has successfully made an important contribution in the theory of partial differential equations and the study of the dynamics of turbulent flows.
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