关于两个球体在Stokes流中解的收敛性问题

Stokes流绕两个球体流动问题是3连通域的外流问题。此问题的解是由一系列调和函数和双调和函数项的级数表达式线形组合而成。文中探讨这些表达式在两个球体接触情况下的收敛性问题。通过收敛性的判断得出了当一个球体向另一个平面接近时，这些解中的系数的级数表达式不收敛；而当两个球体互相接近甚至接触时，其解中的系数的级数表达式收敛。这就为流场中物体的相互接触问题的进一步研究打下了基础。

On convergence of series expressions of the solution to a Stokes flow around two spherical bodies

The investigation of the Stokes flow around two spherical solids is involved in that of the outer flow of the connected regions. The complete solution for the problem is made up of the series expressions of which all terms take the form of harmonics or biharmonics. This paper will discuss the convergence of these series expressions especially when the two spheres are at contact. Using the convergence criterions dealing with the series, it is found that in the case of a sphere approaching a plane, the summation of the corrective coefficients in every series expression becomes divergent, but the summation for the case of two touching spheres is convergent even when the two spheres come into contact. This conclusion lays the foundation for the further investigation of the dynamical process in the case of two bodies in contact.