Project/Area Number  09640227 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
解析学

Research Institution  Meiji University 
Principal Investigator 
MORIMOTO Hiroko School of Science and Technology Professor, 理工学部, 教授 (50061974)

CoInvestigator(Kenkyūbuntansha) 
阿原 一志 明治大学, 理工学部, 講師 (80247147)
服部 晶夫 明治大学, 理工学部, 教授 (80011469)
KATURADA Masashi School of Science and Technology Lecturer, 理工学部, 教授 (80224484)
KONNO Reiji School of Science and Technology Professor, 理工学部, 教授 (20061921)
FUJITA Hiroshi School of Science and Technology Professor, 理工学部, 教授 (80011427)
斎藤 宣一 明治大学, 理工学部, 助手
斉藤 宣一 明治大学, 理工学部, 助手
SAITO Norikazu School pf Science and Technology Assistant

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥3,000,000 (Direct Cost : ¥3,000,000)
Fiscal Year 1998 : ¥1,200,000 (Direct Cost : ¥1,200,000)
Fiscal Year 1997 : ¥1,800,000 (Direct Cost : ¥1,800,000)

Keywords  NavierStokes equations / Boussinesq equations / stationary solutions / general outflow condition / ナヴィエストーク方程式 / フジネスク方程式 / 定常解 / 一般流速条件 / ナヴィエストークス方程式 / ナヴィエ・ストークス方程式 / ブシネスク方程式 
Research Abstract 
The existence of solutions to the stationary NavierStokes equations is known, in general context, only under the stringent outflow condition or for small Raynolds number. We studied the existence of solutions to the stationary NavierStokes equations and of the Boussinesq equations under general outflow condition. We obtained two kinds of results. For arbitrary space dimension and for the boundary value of constant p times gradient of harmonic function, the existence of solution for the above equations is shown except for at most discrete countable case of p. It is to be noted that p can be arbitrary large. For two dimensional case, under the assumption of symmetry, Amick showed the exis tence of solutions. Fujita obtained the concrete construction of the solenoidal symmetric extension of the boundary value in this case. Using this method, Morimoto and Fujita obtained the existence of solutions to the stationary NavierStokes equations in a tubelike domain with inflow and outflow.
