Applied Mathematical Analysis of Fluid Mechanics

流体力学应用数学分析

• 批准号: 11640215
• 负责人: MORIMOTO Hiroko
• 金额: $ 1.79万
• 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: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640215/
• 关键词: Navier-Stokes equations; Boussinesq equations; Stationary solution; General outflow condition; ブシネスク方程式

The problem to find a solution to the Navier-Stokes equations under the general outflow condition is unsolved problem for the domain having multiply connected boundary. It was known for small Reynolds number or under stringent outflow condition. In 1996, H.Morimoto and S.Ukai obtained some results for 2-dimensional annular domain. In 1997, H.Fujita and H.Morimoto studied the n-dimensional domain case with the boundary value which is gradient of a harmonic function and found the existence of solution even for large Reynolds number with some exceptional case, After that, in 1998, for 2-dimensionl symmetric domain, H.Fujita obtained the solenoidal extension of the symmetric boundary value satisfying Leray type inequality and succeeded to obtain an a priori estimate for solutions of Navier-Stokes equations, which proves the existence of solutions. The result was already shown by Ch.Amich in 1984, but the method of Fujita is more practical and useful and is on the way used for stringent outflow condition case. Applying this method for 2-dimensional infinite symmetric channel under general outflow condition, we obtained the follwings. For semi-infinte channel, V shaped channel and Y shaped channel, symmetric and having some finite boundary components, it is shown the existence of a solution satisfying the boundary condition and tending to Poiseuille flows in the infity if the Poiseulle flow is not so strong.

在一般流出条件下求解纳维-斯托克斯方程的问题对于具有多重连通边界的域来说是一个未解问题。它以雷诺数小或流出条件严格而闻名。 1996年，H.Morimoto和S.Ukai获得了一些关于二维环形域的结果。 1997年，H.Fujita和H.Morimoto研究了以调和函数的梯度为边界值的n维域情况，发现即使对于大雷诺数也存在解，但在一些特殊情况下，此后，在1998年，对于二维对称域，H.Fujita 获得了满足 Leray 型不等式的对称边界值的螺线管推广，并成功获得了解的先验估计纳维-斯托克斯方程，证明解的存在性。 Ch.Amich在1984年就已经给出了结果，但Fujita的方法更加实用和有用，并且正在用于严格的流出条件情况。将这种方法应用于一般流出条件下的二维无限对称通道，我们得到了以下结果。对于对称且边界分量有限的半无限通道、V形通道和Y形通道，当泊肃叶流不太强时，存在满足边界条件且趋于无穷大的泊肃叶流的解的存在。

项目成果

H.Morimoto-H.Fujita: "A remarks on the existence of steady Navier-Stokes flowa in 2D semi-infinite channel involving the general outflow condition"Mathematica Bohemica. (to appear).

H.Morimoto-H.Fujita：“关于涉及一般流出条件的二维半无限通道中稳定纳维-斯托克斯流的存在性的评论”Mathematica Bohemica。

H.Fujita: "Non-stationary Stokes flow under leak boundary condition of friction type"Journal of Computing Mathematics. Vol.19 No.1. 1-8 (2001)

H.Fujita：“摩擦型泄漏边界条件下的非平稳斯托克斯流”计算数学杂志。

N.Ishimura and H.Morimoto: "Remarks on the blow-up criterion for 3D Boussinesq equations"M^3AS. 9 (9). 1323-1332 (1999)

N.Ishimura 和 H.Morimoto：“关于 3D Boussinesq 方程的爆炸准则的评论”M^3AS。

R.Konno: "A remark on the Schrodinger-type equation on manifolds, I"明治大学科学技術研究所紀要. 38. 25-32 (1999)

R. Konno：“关于流形上的薛定谔型方程的评论，I”明治大学科学技术研究所通报 38. 25-32 (1999)。

S.Kaneko-H.Fujita: "On Uzawa 's algorithm applied to Stokes flow under boundary condition of friction type"明治大学科学技術研究所紀要. 37. 239-258 (1998)

S. Kaneko-H. Fujita：“论应用于摩擦型边界条件下斯托克斯流的 Uzawa 算法”明治大学科学技术研究所通报 37. 239-258 (1998)。