| Project/Area Number |
24224003
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| Research Category |
Grant-in-Aid for Scientific Research (S)
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Waseda University |
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Principal Investigator |
KOZONO HIDEO 早稲田大学, 理工学術院, 教授 (00195728)
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| Co-Investigator(Kenkyū-buntansha) |
金田 行雄 愛知工業大学, 工学部, 教授 (10107691)
久保 英夫 北海道大学, 理学(系)研究科(研究院), 教授 (50283346)
中村 誠 山形大学, 理学部, 教授 (70312634)
芳松 克則 名古屋大学, 学内共同利用施設等, 准教授 (70377802)
隠居 良行 九州大学, 数理(科)学研究科(研究院), 教授 (80243913)
菱田 俊明 名古屋大学, 多元数理科学研究科, 教授 (60257243)
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| Co-Investigator(Renkei-kenkyūsha) |
OZAWA Tohru 早稲田大学, 理工学術院, 教授 (70204196)
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| Project Period (FY) |
2012-05-31 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥191,100,000 (Direct Cost: ¥147,000,000、Indirect Cost: ¥44,100,000)
Fiscal Year 2016: ¥42,380,000 (Direct Cost: ¥32,600,000、Indirect Cost: ¥9,780,000)
Fiscal Year 2015: ¥37,180,000 (Direct Cost: ¥28,600,000、Indirect Cost: ¥8,580,000)
Fiscal Year 2014: ¥37,180,000 (Direct Cost: ¥28,600,000、Indirect Cost: ¥8,580,000)
Fiscal Year 2013: ¥36,270,000 (Direct Cost: ¥27,900,000、Indirect Cost: ¥8,370,000)
Fiscal Year 2012: ¥38,090,000 (Direct Cost: ¥29,300,000、Indirect Cost: ¥8,790,000)
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| Keywords | ナビエ・ストークス方程式 / 調和解析学 / 関数解析学 / 大域的適切性 / 漸近解析 / 乱流の普遍性 / 情報縮約手法 / 信頼性評価 / Navier-Stokes 方程式 / 流量条件 / 調和ベクトル場 / 漸近安定 / Stokes 方程式 / 最大正則性定理 / Keller-Segel 方程式系 / 自己相似解 / 指数漸近安定 / Leray-Fujita の不等式 / 周期解 / Lax-Milgram の定理 / Garding の不等式 / Besov空間 / Triebel-Lizorkin空間 / Navier-Stokes方程式 / Keller-Siegel方程式系 / compensated compactness / Navier-Stoeks 方程式 / Euler方程式 / Betti数 / 回転流体 / 乱流の普遍原理 / ウェーブレット解析 / 線形応答理論 / エネルギースペクトル |
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| Outline of Final Research Achievements |
The challenging problem on global well-posedness of the Navier-Stokes equations had been so fully investigated that several remarkable results are obtained. Furthermore, our DNS of the uniformly isotropic turbulence is still by far the larger computational performance so that we could deal with the turbulent fluid with the high Reynolds number without any error of the experiment and indeterminacy. Our study has been based on the DNS of such a world highest standard and we could succeed to overcome difficulty of turbulence with the high Reynolds number. In this way, our research projects have developed the modern mathematical analysis, the applied mathematics, computational science and hydrodynamics and hopefully will lead the relevant subjects to the world-wide level.
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| Assessment Rating |
Verification Result (Rating)
A
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Assessment Rating |
Result (Rating)
A: Progress in the research is steadily towards the initial goal. Expected research results are expected.
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