On blowup of gravity-gyroscopic waves with nonlinear sources and sinks on the boundary

In the article, we consider the equation of internal gravity-gyroscopic waves in an exponentially stratified fluid whose model is the great oceans. We study the case in which a fluid occupies a bounded domain and a boundary condition of the third kind is imposed on the boundary, All sinks and sources localized on the boundary are taken into account. The local solvability of the problem in a weak generalized sense is established and sufficient conditions of finite time blowup of solutions are exposed.