Functional-analytic study on incompressible viscous fluid flows

不可压缩粘性流体流动的泛函分析研究

• 批准号: 10440045
• 负责人: MIYAKAWA Tetsuro
• 金额: $ 6.91万
• 依托单位: KOBE UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B).
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-10440045/
• 关键词: Navier-Stokes equations; Initial-boundary value problem; Stability; Asymptotic behavior; Limit theorems; Spectral analysis; Navier-Stokes方程式; 初期値問題; 作用素半群; 作用素の分数べき; Navier-Stokes 方程式; 半群; 中心極限定理; 観測可能量

MIYAKAWA deduced the space-time asymptotic profiles in terms of some Gaussian functions for a specific class of solutions of nonstationary Navier-Stokes equations in the whole space and the half-space, and then applied the results to finding a lower bound of rates of energy decay for general weak solutions. HISHIDA considered flows around a rotating body. He developed perturbation theory for the linearized operator and applied it to finding local-in-time solutions for every square-summable initial data. ADACHI developed spectral analysis for quantum many-body Hamiltonians which have stuctures similar to the above-mentioned linearized operator. His result is concerned with systems involving charged and uncharged particles. FUKUYAMA considered the problem of finding limit distributions for discrete dynamical systems arising from the study of lacunary trigonometric series. He deduced a non-Gaussian limit distribution.

MIYAKAWA在全空间和半空间中推导了一类非平稳Navier-Stokes方程的特定解的高斯函数的时空渐近轮廓，并将结果应用于寻找一般弱解的能量衰减率的下界。HISHIDA考虑了旋转物体周围的流动。他发展了线性化算子的摄动理论，并将其应用于寻找每个平方可和初始数据的局部时间解。ADACHI开发了具有类似上述线性化算子结构的量子多体哈密顿量的谱分析。他的研究结果与涉及带电粒子和不带电粒子的系统有关。FUKUYAMA考虑了由于空三角级数的研究而引起的离散动力系统的极限分布问题。他推导出一个非高斯极限分布。

项目成果

T.Adachi: "Scattering theory for N-body quantum systems in a time-periodic electric field"Funkcialaj Ekvacioj. 44(in press). (2001)

T.Adachi：“时间周期电场中 N 体量子系统的散射理论”Funkcialaj Ekvacioj。

菱田俊明: "The Stokes operator with rotating effect in exterior domains" Analysis. (印刷中).

Toshiaki Hishida：“在外部域中具有旋转效应的斯托克斯算子”分析（正在出版）。

Y.Fujigaki: "Asymptotic profiles of nonstationary incompressible Navier-Stokes flows in the halfspace"Methods and Applications of Analysis. (印刷中). (2001)

Y.Fujigaki：“半空间中非平稳不可压缩纳维-斯托克斯流的渐近轮廓”分析方法和应用（2001 年出版）。

Tetsuro Miyakawa: "Application of Hardy space techniques to the time-decay problem for incompressible Navier-Stokes flows in R^n"Funkcialaj Ekvacioj. 41・1. 383-434 (1998)

Tetsuro Miyakawa：“Hardy 空间技术在 R^n 中不可压缩纳维-斯托克斯流的时间衰减问题中的应用”Funkcialaj Ekvacioj 41・1 (1998)。

T.Miyakawa: "Application of Hardy space techniques to the time-decay problem for incompressible Navier-Stokes flows in R^n" Funkcialaj Ekvacioj. 41. 383-434 (1998)

T.Miyakawa：“Hardy 空间技术在 R^n 中不可压缩纳维-斯托克斯流的时间衰减问题中的应用”Funkcialaj Ekvacioj。