1997 Fiscal Year Annual Research Report

流体力学の応用解析的研究

Research Project

Project/Area Number	09640227
Research Category	Grant-in-Aid for Scientific Research (C)
Research Institution	Meiji University
Principal Investigator	森本浩子明治大学, 理工学部, 教授 (50061974)
Co-Investigator(Kenkyū-buntansha)	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) 桂田祐史明治大学, 理工学部, 講師 (80224484) 今野礼二明治大学, 理工学部, 教授 (20061921) 藤田宏明治大学, 理工学部, 教授 (80011427)
Keywords	ナヴィエ・ストークス方程式 / ブシネスク方程式 / 定常解 / 一般流速条件
Research Abstract	ナヴィエ・ストークス方程式の非斉次境界値問題は一般に、制限された流速条件が成り立つ場合、またはレイノルズ数が小さい場合に解の存在が知られている。我々は、一般流速条件のみを過程してナヴィエ・ストークス方程式およびブシネスク方程式の定常解の存在について研究した。境界値が調和関数のgradientの定数μ倍であるときにブシネスク方程式の定常解の存在が高々可算個の場合を除いて任意のμに対して存在することが示せた。5月に開かれた第1回流体力学の数学解析(京都大学大学院人間環境研究科)および第6回ナヴィエ・ストークス方程式と非線形問題国際会議(パランガ、リトアニア)にて、この結果を発表した。同じく、2次元円環領域におけるブシネスク方程式の定常解の存在が、高々可算個の場合を除いて示せることがわかり6月に開かれたナヴィエ・ストークス方程式理論と数値的方法国際会議(ヴァレンナ、イタリア)にて森本が発表した。また1984年にアミックによって得られた結果(2次元有界領域で直線に関して対称の場合)の構成的証明が藤田により得られ、上記イタリアの学会に招待され講演した。藤田のこの構成的方法は他の問題、外部問題、パイプ状の領域の場合などに有効であることが予想され研究中である。

Research Products
(12 results)

All Other

All Publications (12 results)

[Publications] 森本浩子: "Stationary solultions for the Navier-Stokes equations and the Boussinesg equations under general outflow condition" 京都大学数理解析研究所講究録. 1009. 100-104 (1997)
[Publications] H. Fujita, H. MORIMOTO, H. okamoto: "Stability analysis of the Navier-Stokes flow in annuli" Mathematical Methods in the Applied Sciences. 20. 959-978 (1997)
[Publications] 森本浩子: "円環領域におけるNavier-Stokes方程式の一般流速条件のもとでの境界値問題への注意" 明治大学科学技術研究所紀要. 35. 95-102 (1997)
[Publications] H. Fujita, H. MORIMOTO: "A remark on the existence of the Navier-Stokes flow with non-vanishining outflow condition" GAKUTO Int. Ser. Math, Sci. Appl.10. 53-61 (1997)
[Publications] H. MORIMOTO: "Note on stationary Boussinesq equations ina bounded domain under general outflow condition" Proc. of NSEC 6. (to appear).
[Publications] H. MORIMOTO, S. Ukai: "Perturbation of the Boussinesq flow in an annular domain with general outflow condition" Proc. of International Conference on Navioer-Stokes Equations : Theory and Numerial Methods. (to appear).
[Publications] H. Kawarada, H. Fujita H. Kawarada: "Variational Inequalities for the Navier-Stokes flow coupled with potentional flow through porous medic" Domain Decomposition Methods in Sciences and Engineering (eds Growinski et al). 403-410 (1997)
[Publications] H. Fujita, N. Saito: "An analytical study of optimal speed of convergence of iterations in DDM under certain shape assumptions of domains" Computational Sciences for the 21st Century (eds Lions et al). 139-148 (1997)
[Publications] H. Fujita: "On stationary solutions to Navier-Stokes equations in symmetric plane domains under general ontflow condition" Proc. International Conference on Navier-Stokes Equations : Theory and Numerial Methods. (to appear).
[Publications] H. Fujita, H. Kawarada: "Variational Inequalities for the Stokes equations with boundary conditions of frictions type" Recent Developments in Domain Decompositions Methods and Flow Problems, GAKUO Inter. Ser. Math. Sci. Appl.11(to appear).
[Publications] 服部晶夫: "4-dimensional C-symplectic S -manifolds with non-empty fived point set need not be C-Hamiltonian" Proc. Workshop Geometry and Homotopy, 1997, Warsaw. (to appear).
[Publications] 服部晶夫: "Almost toric manifolds and positive line boundles" Proc. Workshop Geometry and Homotopy, 1997, Warsaw. (to appear).

1997 Fiscal Year Annual Research Report

流体力学の応用解析的研究

Principal Investigator

森本 浩子 明治大学, 理工学部, 教授 (50061974)

Research Products

[Publications] 森本浩子: "Stationary solultions for the Navier-Stokes equations and the Boussinesg equations under general outflow condition" 京都大学数理解析研究所講究録. 1009. 100-104 (1997)

[Publications] H. Fujita, H. MORIMOTO, H. okamoto: "Stability analysis of the Navier-Stokes flow in annuli" Mathematical Methods in the Applied Sciences. 20. 959-978 (1997)

[Publications] 森本浩子: "円環領域におけるNavier-Stokes方程式の一般流速条件のもとでの境界値問題への注意" 明治大学科学技術研究所紀要. 35. 95-102 (1997)

[Publications] H. Fujita, H. MORIMOTO: "A remark on the existence of the Navier-Stokes flow with non-vanishining outflow condition" GAKUTO Int. Ser. Math, Sci. Appl.10. 53-61 (1997)

[Publications] H. MORIMOTO: "Note on stationary Boussinesq equations ina bounded domain under general outflow condition" Proc. of NSEC 6. (to appear).

[Publications] H. MORIMOTO, S. Ukai: "Perturbation of the Boussinesq flow in an annular domain with general outflow condition" Proc. of International Conference on Navioer-Stokes Equations : Theory and Numerial Methods. (to appear).

[Publications] H. Kawarada, H. Fujita H. Kawarada: "Variational Inequalities for the Navier-Stokes flow coupled with potentional flow through porous medic" Domain Decomposition Methods in Sciences and Engineering (eds Growinski et al). 403-410 (1997)

[Publications] H. Fujita, N. Saito: "An analytical study of optimal speed of convergence of iterations in DDM under certain shape assumptions of domains" Computational Sciences for the 21st Century (eds Lions et al). 139-148 (1997)

[Publications] H. Fujita: "On stationary solutions to Navier-Stokes equations in symmetric plane domains under general ontflow condition" Proc. International Conference on Navier-Stokes Equations : Theory and Numerial Methods. (to appear).

[Publications] H. Fujita, H. Kawarada: "Variational Inequalities for the Stokes equations with boundary conditions of frictions type" Recent Developments in Domain Decompositions Methods and Flow Problems, GAKUO Inter. Ser. Math. Sci. Appl.11(to appear).

[Publications] 服部晶夫: "4-dimensional C-symplectic S -manifolds with non-empty fived point set need not be C-Hamiltonian" Proc. Workshop Geometry and Homotopy, 1997, Warsaw. (to appear).

[Publications] 服部晶夫: "Almost toric manifolds and positive line boundles" Proc. Workshop Geometry and Homotopy, 1997, Warsaw. (to appear).

森本浩子明治大学, 理工学部, 教授 (50061974)