THE EIGENFUNCTIONS OF THE STOKES OPERATOR IN SPECIAL DOMAINS .2.

We investigate the eigenvalue problem of the Stokes operator in an ope n bounded rectangular parallelepiped of the R-3 supplemented with homo geneous Dirichlet boundary conditions on two face to face lying latera l surfaces and periodical conditions in the directions orthogonal to t he other faces. By separation we deduce a corresponding system of ordi nary differential equations. We look for solutions as solenoidal vecto r fields satifying the boundary conditions. The investigation of possi ble cases yields either the explicit eigenfunctions and eigenvalues or equations for determining the eigenvalues and a general deduced form of the eigenfunctions. In the appendix rue give an example of the firs t eigenvalues of the Stokes operator for fixed l = 2.69.