Аннотация:In this paper, we consider the equation of internal gravitational-gyroscopic waves in an exponentially stratified fluid whose model can be the World Ocean. We investigate the case when this fluid occupies a bounded domain, and we impose a boundary condition of the third kind on the boundary. We take into account the `sources' and `sinks' localized on the boundary. We prove the local solvability of the problem in a weak generalized sense and obtain sufficient conditions for the finite-time blow-up of the solution