Project/Area Number  08454028 
Research Category 
GrantinAid for Scientific Research (B)

Section  一般 
Research Field 
解析学

Research Institution  KYOTO UNIVERSITY 
Principal Investigator 
OKAMOTO Hisashi RIMS,KYOTO UNIVERSITY Professor, 数理解析研究所, 教授 (40143359)

CoInvestigator(Kenkyūbuntansha) 
TAKEI Yoshitsugu RIMS,KYOTO UNIVERSITY Assistant Professor, 数理解析研究所, 助教授 (00212019)
MUROTA Kazuo RIMS,KYOTO UNIVERSITY Professor, 数理解析研究所, 教授 (50134466)
MIWA Tetsuji RIMS,KYOTO UNIVERSITY Professor, 数理解析研究所, 教授 (10027386)
KASHIWARA Masaki RIMS,KYOTO UNIVERSITY Professor, 数理解析研究所, 教授 (60027381)
KAWAI Takahiro RIMS,KYOTO UNIVERSITY Professor, 数理解析研究所, 教授 (20027379)

Project Fiscal Year 
1996 – 1996

Project Status 
Completed(Fiscal Year 1996)

Budget Amount *help 
¥5,900,000 (Direct Cost : ¥5,900,000)
Fiscal Year 1996 : ¥5,900,000 (Direct Cost : ¥5,900,000)

Keywords  Equations of motion of fluids / singular perturbation / algebraic analysis / matroid theory / vortex sheet / numerical method / 流体方程式 / 特異摂動 / 代数解析 / マトロイド理論 / 渦層 / 数値解析法 
Research Abstract 
H.Okamoto discovered some new exact solutions of the NavierStokes equations which shed light on the singular perturbation analysis of the equations. One of them is a generalization of stagnationpoint flows of Tamada and Dorrepaal which converges on a wall obliquely. Other solutions include those solutions which satisfy Leray's similarity equations. Among others, he found those solutions which are represented by the confluent hypergeometric functions. He also studied the stability of certain stationary NavierStokes equations which satisfy the inflow / outflow boundary condition. Some the solutions are proved to be stable for all the Reynolds number, which is a surprising results. By the vortex method, Okamoto and Sakajo computed numerically the vortex sheet in shear flows. Some interesting interactions between vortex sheet and shear are discovered. T.Kawai and Y.Takei studied, via the algebraic analysis method, a certain aspect of singular perturbation theory of the Painleve equations. Their theory will be published in their book entitled "Algebraic Analysis of Singular Perturbation" (in Japanese) from Iwanami Shoten. K.Murota and S.Iwata made a contribution to the present study through the theory of numerical linear algebra. Some singular perturbation problem leads to a very illconditioned matrix problem after a suitable discretization. The techniques developed by them are very helpful when we solve such illconditioned matrix problem. Murota proposes many methods which leads to better accuracy and speedup of the computation.
