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: 10440055
• 负责人: MASUDA Kyuya
• 金额: $ 5.63万
• 依托单位: Meiji University (1999)Tohoku University (1998)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10440055/
• 关键词: Navier-Stokes equations; Magnetic fluid; Reaction-Diffusion equations; 分岐理論; 特異摂動

(1) Masuda's Results : He could show the existence of solutions of Navier-Stokes equations in continuous function space.(2) The result of Masuda and Kenmotsu : They could classify completely the minimal surfaces of constant Gaussian curvature in two-dimensional complex form.(3) Morimoto's results : she could show the existence of solutions of two dimensional stationary Navier-Stokes equations with general outlet boundary with general outlet boundary condition forsome symmetric domain. Also, she could show the existence of solutions for stationary Boussinesq equations with general outlet boundary condition.(4) Tani's results : he could show the classical solvability of the Stefan problem in a viscous incompressible fluid flow. Also, he could solve a free boundary problem for an incompressible ideal fluid in two space dimensions.(5) The result of Ishimura and Nakamura : They could show the convergence of attracters for simplified magenetic Benard system.

(1)Masuda的结果：他可以证明连续函数空间中的Navier-Stokes方程解的存在性。(2)Masuda和Kenmotsu的结果：他们可以完全地将二维复形式的常高斯曲率极小曲面分类。(3)Morimoto的结果：她可以证明具有一般出口边界的二维定常N-S方程在某些对称区域上具有一般出口边界条件的解的存在性。此外，她还证明了具有一般出口边界条件的定常Boussinesq方程的解的存在性。(4)Tani的结果：他可以证明粘性不可压缩流体流动中Stefan问题的经典可解性。此外，他还可以解决二维不可压缩理想流体的自由边界问题。(5)Ishimura和Nakamura的结果：他们可以证明简化的磁生Benard系统的吸引子的收敛。

项目成果

N.Ishimura: "On the structure of steady solutions for the kinematic model of spiral waves in excitable media"Japan J.Indust. Appl. Math. 15. 317-330 (1998)

N.Ishimura：“关于可激发介质中螺旋波运动学模型的稳定解的结构”日本工业杂志。

N. Nakamura: "Numerical analysis of Eguchi-Oki-Matsumura equations"Proceedings of Fouth Japan-China Joint Seminar on Numerical Mathematics, Gakuto International Series, Mathematical Science and Applications. 12. 213-222 (1999)

N. Nakamura：《Eguchi-Oki-Matsumura方程的数值分析》第四届日中数值数学联合研讨会论文集，学人国际丛书，数学科学与应用。

N.Isimura: "Self-fimilar solutions for the Gauss curvature evolution of rotationally symmetric surfaces"Nonlinear Analysis T.M.A. 33. 97-104 (1998)

N.Isimura：“旋转对称表面高斯曲率演化的自相似解”非线性分析 T.M.A.

N.Ishimura and M.Nakamura: "Characterization on the long time behavior of 2D Navier-Stokes equations" Pittman Research Notes in Math.Series. 388. 38-44 (1998)

N.Ishimura 和 M.Nakamura：“二维纳维-斯托克斯方程长期行为的表征”Math.Series 中的皮特曼研究笔记。

K, Masuda: "Non-existence of nontrivial solution of some nonlinear elliptic equations"Nonlinear Analysis, T. M. A.. (2001)

K, Masuda：“某些非线性椭圆方程的非平凡解的不存在性”非线性分析，T. M. A.. (2001)