The Stokes Eigenvalue Problem on balls and annuli in three dimensions: Solutions with Poloidal and Toroidal Fields

We consider the Stokes eigenvalue problem in open balls and open annuli in R3 with homogeneous Dirichlet boundary conditions. Using the frame of toroidal and poloidal fields we construct the othogonal decomposition of the Stokes eigenvalue problem in problems for toroidal and poloidal eigenfunctions. This provides the proof of the completeness of a system of explicitly calculated Stokes eigenfunctions given by one of the authors in 1999, [14].