Sufficient conditions of non-almost-periodicity for the solutions of S. L. Sobolev's equation (Q811286)

The author reports the results of a study of the Sobolev equation \((\partial^ 2/\partial t^ 2)\Delta p+4\omega^ 2(\partial^ 2p/\partial z^ 2)=0\) describing small oscillations of an ideal fluid occupying a vessel rotating about z-axis with angular velocity \(\omega\) ; p denotes the hydrostatic pressure. The problem of the existence of a non almost periodic solution of the Sobolev equation can be reduced to a spectral problem for a bounded self-adjoint nonnegative operator in a Sobolev functional space. By using some a priori estimates for the solution, the author investigates the corresponding spectral problem and gives explicit sufficient conditions for non almost periodicity of the solution.