2011 Fiscal Year Final Research Report
Applied Analysis on the Navier-Stokes Equations and Related Dynamical Systems
| Project/Area Number |
20244006
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
YAMADA Michio 京都大学, 数理解析研究所, 教授 (90166736)
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| Project Period (FY) |
2008 – 2011
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| Keywords | ナヴィエ-ストークス方程式 / 解の特異点 / 解の爆発 |
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| Research Abstract |
The Navier-Stokes equations and the Euler equations are the master equations of the fluid mechanics. We searched for singularity and pseudo singularity. The Proudman. Johnson equation and reaction-diffusion equation with integral constraint were studied. By numerically computing solutions, we found that a topologically simple solutions exists and they exist only in two-dimensional Navier-Stokes equations and those closely related to it.
Trajectories of fluid particles in a progressive water-waves were computed. What is called the Stokes drift was proved mathematically. Our proof is simpler than any other proof and easily adapted to the numerical computation. Our numerically method enables us to compute not only the gravity waves but also capillary-gravity waves.
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