Study on Navier-Stokes equations and related nonlinear partial differential equations

纳维-斯托克斯方程及相关非线性偏微分方程研究

• 批准号: 12640223
• 负责人: MASUDA Kyuya
• 金额: $ 2.11万
• 依托单位: Meiji University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640223/
• 关键词: Navier Stokes equations; Schroedinger operators; Minimal surfaces; Kuramoto-Syvashinsky equations; Stefan problem; general slip boundary condition; curvature equation; infinite channel; オイラー方程式; 解析性; ナヴィエ・ストークス方程式; 磁気流体; 反応・拡散系

Masuda succeeded in classifying completely the minimal surfaces of constant Gaussian curvature in two-dimensional complex formMorimoto showed the existence of solutions of two dimensional stationary Navier Stokes equations with general outlet boundary condition for some symmetric domain of channel type. Konno showed the non-existence of positive eigen-value for Schroedinger operator in the square integrable function space on unbounded domain. Ishimura and Nakamura found some important properties for the Kuramoto-Shivashinsky equations. Tani showed the existence of solutions of Navier-Stokes equations under the general slip boundary conditions.

增田成功地将二维复形式的常高斯曲率极小曲面完全分类，Morimoto证明了具有一般出口边界条件的二维定常Navier-Stokes方程解的存在性。Konno证明了无界区域上平方可积函数空间中Schroedinger算子不存在正特征值。石村和中村发现了Kuramoto-Shivashinsky方程的一些重要性质。Tani证明了一般滑移边界条件下Navier-Stokes方程解的存在性。

项目成果

Tani, A., Itoh, H.: "The initial problem for the non-homogeneous Navier-Stokes equations general slip boundary condition"Proc. Royal Soc. Edinburgh. 130. (2000)

Tani, A., Itoh, H.：“非齐次 Navier-Stokes 方程一般滑移边界条件的初始问题”Proc。

Morimoto, H. and Fujita, H.: "On stationary Navier-Stokes flows in 2D semi-infinite channel involving the general outflow condition"Ann. Univ.. Ferra-Sez.VII-Sc.Mat.XLVI. 285-290 (2000)

Morimoto, H. 和 Fujita, H.：“涉及一般流出条件的二维半无限通道中的稳态纳维-斯托克斯流”Ann。

増田 久弥: "応用解析"シュプリンガー東京. 600 (2002)

Hisaya Masuda：“应用分析”Springer 东京 600 (2002)。

H.Morimoto-H.Fujita: "Stationary Navier-Stokes flow in 2-dimensional V-shaped infinite channel under general outflow condition"Topics in Mathematical Fluid Dynamics. (to appear).

H.Morimoto-H.Fujita：“一般流出条件下二维V形无限通道中的稳态纳维-斯托克斯流”数学流体动力学专题。

Masuda, K., Kenmotsu, K.: "On minimalsurfaces of constant curvature in two-dimensional complex space form"J. reine angew. Math.. 523. 69-101 (2000)

Masuda, K.、Kenmotsu, K.：“关于二维复空间形式中恒定曲率的最小表面”J.