Abstract
An initial-boundary value problem is considered for the equation which describes the vibrations of an ideal, stratified liquid occupying the lower half space in the Boussinesq approximation. The Vaisala-Brunt frequency is assumed to be constant. The boundary condition on the planar boundary is a combination of the conditions on the solid cover and the free surface and, moreover, the latter contains a term which takes account of capillarity. A formulation of the problem is given, its solution is constructed and its behaviour at long times is investigated.
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