On free oscillations of a rotating viscous liquid outer core of the Earth
We consider a spherical shell of a viscous fluid modeling the outer core of the Earth. We construct a basis consisting of Laplacian eigenfields vanishing at the boundaries of the shell. It is shown that the Laplacian eigenfields ordered by their (increasing) eigenvalues, are also ordered in the same way by their oscillatory vigor. This basis is also used for a simple proof (based on the Carleman theorem) demonstrating that the eigenfields and associated fields of the operator in the problem of free oscillations of a viscous spherical shell under small deviations from solid-body rotation constitute a complete set.