境界が非有界な領域での粘性流体の挙動の研究

无界区域粘性流体行为研究

• 批准号: 18340046
• 负责人: 宮川 鉄朗
• 金额: $ 9.98万
• 依托单位: Kanazawa University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2006
• 资助国家: 日本
• 起止时间: 2006 至 2008
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18340046/
• 关键词: 安定性; 初期値問題; 漸近挙動; 渦; 自由境界; ナヴィエ・ストークス方程式; 非有界領域; 水面波

代表者宮川は,半空間での流れの研究の基礎になるべクトル場の分解定理の完全な証明を与えた.これは次年度以降に実施予定の半空間における流れの漸近展開の研究の出発点となるものであるが,従来の証明の記述は不完全なものであった.分担者菱田は回転物体周囲の流れの初期値境界値問題について,線形化作用素のスペクトルを完全に決定し,さらにその結果を用いて元の初期値境界値問題の解の構成に成功した.この問題自身は,境界が有界な領域を扱っているが,無限遠での解の挙動の分析に基づく基礎的関数空間の設定が,非有界な境界をもつ領域での流れの研究に極めて重要な技術的手順を示唆する.すなわち本問題では定常解の空間無限遠での挙動が極めて特異であり,その結果として線形化方程式からより扱いやすい線形化作用素を抽出するという作業が必要になる.菱田の仕事はこの手順の注目すべき成功例であり,他の問題の処理に益するところが極めて大きいと期待できる.分担者井口は表面張力と重力の効果を考慮した自由表面波の伝播問題を扱い,表面張力係数がある臨界数に極めて近い場合にいわゆる長波近似を実行して,近似方程式として標準的に用いられてきた浅水波方程式に無視できない補正が必要なことを指摘し,実際にその補正項を導出した.分担者畑上は,交通流の流体モデルを用いて渋滞形成の解析を行った.多重車線と車線変更を考慮したモデルを導入し,生起するパターンの安定性を解析した.

Representative Yoshikawa, a representative of the study of half-space mass flow, is based on the decomposition Theorem of the theory of decomposition. In the coming year, the application of the half-space air flow system has been carried out in the near future, and the research has been carried out to show that the records are not complete. The distributor Lingtian returns the boundary problem of the object in the early stage of the flow problem, and the morphing agent is completely determined. The result is that the solution of the realm problem in the early stage of the object has been successfully solved. The problem is of its own nature, the boundary is limited, and there is no limit to the number of space settings of the basic system of mobile analysis. there is no boundary, and there is no limit to the number of space settings of the basic data base, the non-boundary boundary, the domain, the research, the flow, the research, the important technology and the device. There is no limit to the solution of this problem. the results show that the equation does not affect the shape of the problem. in this case, there is no limit to the solution of this problem. Mr. Lingtian paid close attention to the success stories of Mr. Yamada, and he was looking forward to hearing from him. The distributor of the wellhead surface force and gravity wave is responsible for the propagation of free surface waves, and the boundary number of the surface force is very close to that of the long wave. The shallow water wave equation based on the standard of the approximate equation does not show that it is necessary to criticize the wave, and the standard of the approximate equation is that the wave equation of the shallow water does not need to be criticized. The contributor goes up, and the traffic flow, the fluid flow, forms the analytical line with the delay. The multi-line connection line is more effective, which leads to the analysis of the stability.

项目成果

Nonstationary navier-stokes flows in a two-dimensional exterior domain with rotational symmetries

• DOI: 10.1512/iumj.2006.55.2726
• 发表时间: 2006
• 期刊: Indiana University Mathematics Journal
• 影响因子: 1.1
• 作者: Cheng He;Tetsuro Miyakawa

$L^q$ estimates of weak solutions to the stationary Stokes equations around a rotating body

• DOI: 10.2969/jmsj/1156342036
• 发表时间: 2006-07
• 作者: T. Hishida

On two-dimensional Nevier-Stokes flows with rotational symmetries

具有旋转对称性的二维内维-斯托克斯流

• 发表时间: 2006
• 期刊: Funkcialaj Ekvacioj 49
• 作者: H. Kawasaki;J. Sato;三上敏夫;J. Sato;Shuichi Sato;T. Iguchi;H. Hyakutake;竹田雅好;Cheng He
• 通讯作者: Cheng He

D' Alembert's paradox and the integrability of pressure for two? dimensional Euler flows in an exterior domain

达朗贝尔悖论和两个压力的可积性？

• 发表时间: 2006
• 期刊: Kyushu Journal of Mathematics 60
• 作者: H. Kawasaki;J. Sato;三上敏夫;J. Sato;Shuichi Sato;T. Iguchi;H. Hyakutake;竹田雅好;Cheng He;Akihiko Miyachi;Cheng He;竹田雅好;S. Iwamoto;Akihiko Miyachi;Tetsuro Miyakawa
• 通讯作者: Tetsuro Miyakawa

Linear and nonlinear stability of a vortex ring

涡环的线性和非线性稳定性

• 发表时间: 2006
• 期刊: Proceedings of IUTAM symposium on elementary vortices and coherent structures
• 作者: 0.~Hashimoto;H.~Tamura;H.Tamura;H.Tamura et al.;H.Tamura et al.;T.Koike et al.;May Thi Tun;Y. Fukumoto;S. Lugomer;Cheng He;Cheng He;Tetsuro Miyakawa;Yasuhide Fukumoto
• 通讯作者: Yasuhide Fukumoto