The Eigenfunctions of the Stokes Operator in Special Domains. III
D.-S. Lee, Bernd Rummler · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 2002
We consider the eigenvalue problem of the Stokes operator in a bounded domain of R3 bounded by two concentrical cylinders with homogeneous Dirichlet boundary conditions on the curved part of the boundary and periodical conditions in along the cylinder axis (in x1-direction). We deduce by separation the correspondent systems of ordinary differential equations and solve them explicitly looking for solenoidal vector fields fulfilling the boundary conditions. The investigation of possible cases yields either the explicit eigenfunctions and eigenvalues or equations for the determination of the eigenvalues and a general representation of the eigenfunctions. The completeness of the calculated system of eigenfunctions in S can be proven analogously to [9].