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.

在一般外流条件下求解Navier-Stokes方程的问题是多连通边界区域的未解问题。这是已知的小雷诺数或严格的流出条件下。1996年，H.Morimoto和S.Ukai获得了二维环形域的一些结果。1997年，H.Fujita和H.Morimoto研究了n维区域的边界值为调和函数梯度的情形，并在某些例外情况下发现了大Reynolds数下解的存在性。H.Fujita得到了满足Leray型不等式的对称边值的螺线管延拓，并成功地得到了Navier方程解的先验估计，Stokes方程，证明了解的存在性。Ch.Amich在1984年已经给出了结果，但Fujita的方法更实用，并且正在用于严格流出条件的情况。将此方法应用于一般出流条件下的二维无限大对称槽道，得到了如下结果。对于半无限长、V形和Y形对称的具有有限边界分量的通道，当Poiseulle流不是很强时，证明了满足边界条件的解的存在性，并在无限域内趋于Poiseulle流.

项目成果

H.Morimoto-H.Fujita: "A remark on the exstence of steady Navier-Stokes flows 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。

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。

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)。