Mathematical Theory of turbulence by the method of modern analysis and computational science

2016 Fiscal Year Final Research Report

• Project/Area Number: 24224003
• Research Category: Grant-in-Aid for Scientific Research (S)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Waseda University
• Principal Investigator: KOZONO HIDEO 早稲田大学, 理工学術院, 教授 (00195728)
• 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)
• Co-Investigator(Renkei-kenkyūsha): OZAWA Tohru 早稲田大学, 理工学術院, 教授 (70204196)
• Project Period (FY): 2012-05-31 – 2017-03-31
• 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

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.

Free Research Field

偏微分方程式論，非線形解析学