Mathematical research on mechanical problems of incompressible fluid
| Project/Area Number |
18H01137
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Review Section |
Basic Section 12040:Applied mathematics and statistics-related
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| Research Institution | Gakushuin University |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥11,700,000 (Direct Cost: ¥9,000,000、Indirect Cost: ¥2,700,000)
Fiscal Year 2021: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2020: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2019: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2018: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
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| Keywords | Navier-Stokes equations / 非線形偏微分方程式 / 流体力学 / 水面波 / Prandtl-Batchelor theory / 精度保証計算 / 水面波の解析 / ナヴィエ・ストークス方程式 / Navier-Stokes方程式 / 数値計算法 / 数理流体力学 / 数値解析学 / Navier-Stokes 方程式 |
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| Outline of Final Research Achievements |
The Kolmogorov problems for the two-dimensional Navier-Stokes equations was studied and a kind of universal patterns for large vortices were confirmed by the numerical experiments. Water-waves on two vortical layers were computed numerically, and many highly nontrivial solutions of many stagnation points were discovered.New method of computing the blow-up time for nonlinear parabolic equations were proposed.
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| Academic Significance and Societal Importance of the Research Achievements |
特異摂動の問題に極めて不思議な解が存在することを数値実験で確かめた。それを保証する数学的な理論も部分的に提出された。しかし、完全な解決には程遠い。これらは次の世代への問題と言うことができる。特にプラントル・バチェラー理論の一般化には大きな魅力を感じる。
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Report
(5 results)
Research Products
(22 results)
