Abstract
AbstractThe famous classical S. Krein problem of small motions and normal oscillations of a viscous fluid in a partially filled container is investigated by a new approach based on a recently developed theory of operator matrices with unbounded entries. The initial boundary value problem is reduced to a Cauchy problem in some Hilbert space. The operator matrix 𝒜 is a maximal uniformly accretive operator which is selfadjoint in this space with respect to some indefinite metric. The theorem on strong solvability of the hydrodynamic problem is proved. Further, the spectrum of normal oscillations, basis properties of eigenfunctions and other questions are studied.
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