Applied Mathematical Analysis of Fluid Mechanics

流体力学应用数学分析

• 批准号: 09640227
• 负责人: MORIMOTO Hiroko
• 金额: $ 1.92万
• 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: 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-09640227/
• 关键词: Navier-Stokes equations; Boussinesq equations; stationary solutions; general outflow condition; ナヴィエストークス方程式; ナヴィエ・ストークス方程式; ブシネスク方程式

The existence of solutions to the stationary Navier-Stokes equations is known, in general context, only under the stringent outflow condition or for small Raynolds number. We studied the existence of solutions to the stationary Navier-Stokes equations and of the Boussinesq equations under general outflow condition. We obtained two kinds of results. For arbitrary space dimension and for the boundary value of constant p times gradient of harmonic function, the existence of solution for the above equations is shown except for at most discrete countable case of p. It is to be noted that p can be arbitrary large.For two dimensional case, under the assumption of symmetry, Amick showed the exis tence of solutions. Fujita obtained the concrete construction of the solenoidal symmetric extension of the boundary value in this case. Using this method, Morimoto and Fujita obtained the existence of solutions to the stationary Navier-Stokes equations in a tube-like domain with inflow and outflow.

在一般情况下，只有在严格的流出条件下或小雷诺数下，才知道平稳Navier-Stokes方程解的存在性。研究了一般外流条件下稳态Navier-Stokes方程和Boussinesq方程解的存在性。我们得到了两种结果。对于任意空间维数，对于常p乘以调和函数梯度的边值，除p的至多离散可数情况外，均证明上述方程解的存在性。需要注意的是，p可以任意大。对于二维情况，在对称假设下，Amick证明了解的存在性。Fujita在这种情况下得到了边值的螺线线对称扩展的具体构造。利用该方法，Morimoto和Fujita得到了具有流入和流出的管状区域内平稳Navier-Stokes方程解的存在性。

项目成果

H.Fujita and H.Morimoto: "A remark on the existence of the Navier-Stokes flow with non-vanishing outflow condition" Gakuto International Series Mathematical Science and Applications. Vol.10. 53-61 (1997)

H.Fujita 和 H.Morimoto：“关于具有非零流出条件的纳维-斯托克斯流的存在性的评论”学人国际系列数学科学与应用。

R.Konno: "Growth estimate of generalized eigenfunctions of DELTA on two dimensional manifolds" Research Reports School of Science and Technology Meiji University. No.19. 65-75 (1998)

R.Konno：“二维流形上 DELTA 广义本征函数的增长估计”研究报告明治大学理工学院。

H. Fujita, N. Saito: "An analytical study of optimal speed of convergence of iterations in DDM under certain shape assumptions of domains" Computational Sciences for the 21st Century (eds Lions et al). 139-148 (1997)

H. Fujita、N. Saito：“在域的某些形状假设下对 DDM 中迭代收敛的最佳速度的分析研究”《21 世纪计算科学》（Lions 等人编辑）。

H.Morimoto: "Note on stationary Boussinesq equations in a bounded domain under general outflow condition" Proceedings of NSEC6, Ed.Amann, Galdi, Pileckas, Sol-lonikov. 183-193 (1998)

H.Morimoto：“一般流出条件下有界域中的平稳 Boussinesq 方程的注释”NSEC6、Ed.Amann、Galdi、Pileckas、Sol-lonikov 的论文集。

N.Saito: "On the shape of domains and the speed of convergence in the certain DDM for the Stokes equation" Abstracts of 4th Japan-China Sem.on Numer.Math.25-28 (1998)

N.Saito：“论斯托克斯方程的特定 DDM 中的域形状和收敛速度”第四届中日数学学会摘要 25-28 (1998)