0rr-Sommerfeld方程的特征值问题及展开定理

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The Eigenvalue Problem and Expansion Theorems Associated with Orr-Sommerfeld Equation

摘要: Orr-Sommerfeld方程的特征值问题及展开定理,对于研究流体层流稳定问题具有重要意义,因此,有不少作者研究过.但据文献[6],这一问题还不能认为已完全解决.因此在本文中,我们进一步研究了这一问题,得到的具体结果是:展式的系数满足一个Paley-Wiener型不等式,它是通常完备正交系展式系数所满足的Bessel等式的一个推广:而且证明了展式是绝对一致收敛的.

Abstract: The eigenvalue problem and expansion theorems associated with Orr-Sommerfeld equation,which is fundamental for the investigation of the problem of stability of laminar fluid motion,have been investigated by several authors,but the results are still imcomplete[6].In this paper,this problem is reinvestigated,and some new results are obtained,which are;(1)The expassion series converges not only uniformly but also absolutely;(2)The coefficients of the expansion series satisfy an inequality of Paley-Wiener type,which is the natural extension of the well known Bessel equality of a complete orthogonal set.

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