Axially symmetric motion of rigid circular ring in Stokes flow (Q2755243)

Using the Mehler-Fok transformation, author constructs in toroidal coordinates a solution of axially symmetric problem of Stokes flow around a rigid circular plate. The problem is reduced to a coupled system of integral equations, and then to a Fredholm integral equation of the second kind with kernel \(K(x,t)=(t+x)/{\text sh}{t+x\over2}-(t-x)/{\text sh}{t-x\over2}\). For the case of wide rings, this kernel is replaced by the kernel \(-0.3(t\,{\text sh}(x/2)+x\,{\text sh}(t/2)\), and practically explicit solution is derived.