Clarification of the mathematical structure of fluid-dynamical and electromagnetic phenomena depending on topological properties of the domain.

根据域的拓扑特性阐明流体动力学和电磁现象的数学结构。

• 批准号: 21540179
• 负责人: YANAGISAWA Taku
• 金额: $ 2.25万
• 依托单位: Nara Women's University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540179/
• 关键词: 関数方程式; 境界値問題; Hodge分解; ナビエ・ストークス方程式; 磁気流体力学方程式; Navier-Stokes方程式; 分解定理; Div-Curl lemma; 流体力学

Several phenomena of fluid or electromagnetism seem to have close relation to topological properties of the domain in which the phenomena occur. Here the topological properties of the domain mean, for example, the number of the inner boundary components and the genus of the outer boundary component of the domain. This research discusses new analytical methods based on the decomposition theorem of vector fields on the domain and the singular perturbation, aiming at clarifying the mathematical structure of such fluid-dynamical and electromagnetic phenomena depending on topological properties of the domain.

流体或电磁的几种现象似乎与发生这些现象的域的拓扑特性密切相关。这里，域的拓扑性质是指，例如域的内边界分量的数量和外边界分量的亏格。本研究讨论了基于域上矢量场分解定理和奇异摄动的新分析方法，旨在阐明此类取决于域拓扑性质的流体动力学和电磁现象的数学结构。

项目成果

Analyticity for higher order nonlinear disiersive equations

高阶非线性离散方程的解析性

• 发表时间: 2010
• 作者: N.Hayashi

Boundary value problems of the stationary MHD equations and Navier-Stokes equations with Coriolis force

具有科里奥利力的平稳MHD方程和纳维-斯托克斯方程的边值问题

• 发表时间: 2011
• 作者: Taku Yanagisawa

Leray's problems on the stationary Navier-Stokes equations with inhomogeneous boundary data I

具有非齐次边界数据 I 的平稳纳维-斯托克斯方程的 Leray 问题

• 发表时间: 2009
• 作者: 柳沢卓

Leray's inequality in general multi-connected domains in R^n

R^n 中一般多连通域中的 Leray 不等式

• 发表时间: 2011
• 作者: H.Kozono

Analyticity for higher order nonlinear dispersive equations

高阶非线性色散方程的解析性

• 发表时间: 2010
• 作者: N. Hayashi; K. Tomoeda; T. Yanagisawa
• 通讯作者: T. Yanagisawa