Variational Problems in Differential Geometry

微分几何中的变分问题

• 批准号: 09440030
• 负责人: NAITO Hisashi
• 金额: $ 9.15万
• 依托单位: Nagoya University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09440030/
• 关键词: Heat Flow; Yang-Mills connection

In this research, we study a behavior of solutions of Yang-Mills heat flow on compact 4-manifolds. We obtain result which is a type of "small data global existence".It is well-known that there exists the lower bound of the energy of smooth connections over compact 4-manifolds. The bound is determined by the topological invariant of the pricipal bundle. In this research, we prove that if the energy of the initial data is close to the bound, then there exists a time-global smooth solution of the Yang-Mills heat flow.

在本研究中，我们研究了紧凑 4 流形上的 Yang-Mills 热流解的行为。我们得到的结果是一种“小数据全局存在”。众所周知，紧四流形上的平滑连接存在能量下界。界限由主丛的拓扑不变量确定。在这项研究中，我们证明，如果初始数据的能量接近界限，则存在杨-米尔斯热流的时间全局平滑解。

项目成果

H.Kozono and H.Sohr: "Regularity criterion of weak solutions to the Navier-Stokes equations" Adv.Differential Equations. 2. 535-554 (1997)

H.Kozono 和 H.Sohr：“纳维-斯托克斯方程弱解的正则性准则”Adv.Differential Equations。

H.Tanigawa: "Grafting harmonic maps and hyperbolic surgaces" J.Differentail Geom.47. 399-419 (1997)

H.Tanikawa：“嫁接调和图和双曲线曲面”J.Differentail Geom.47。

H.Tanigawa: "Grafting, harmonic maps and hyperbolic surfaces" J.Differentail Geom.47. 399-419 (1997)

H.Tanikawa：“嫁接、调和映射和双曲曲面”J.Differentail Geom.47。

H.Tanigawa: "Grafting,harmonic maps and hyperbolic surfaces" J.Differentail Geom.47. 399-419 (1997)

H.Tanikawa：“嫁接、调和映射和双曲曲面”J.Differenttail Geom.47。

H.Kozono,H.Sohr and M.Yamazaki: "Representation formula,net force and energy relations to the stationally Navier-Stokes equa-tions in 3-dimensional exterior domains" Kyusyu J-.Math. 51. 239-260 (1997)

H.Kozono，H.Sohr 和 M.Yamazaki：“3 维外部域中稳态纳维-斯托克斯方程的表示公式、净力和能量关系”Kyusyu J-.Math。