EXISTENCE OF SMALL OSCILLATIONS IN A CYLI NDRICAL LIQUID COLUMN WITH ZERO-GRAVITY

The author considers a column of inviscid incompressible liquid under zero gravity contained in a infinitely long cylindrical container, wit h an arbitrary cross-section. When the container is fixed, there is an equilibrium position of the liquid, the free surface being a circular cylinder. Using a classical method of the functional analysis, he pro ves the existence of small oscillations of the liquid about this posit ion. When the container is in uniform rotation, it is necessary to app ly a new method. From a variational formulation of the problem, the au thor proves, by means of semi-groups theory, the existence of small os cillations of the liquid, for an arbitrary angular velocity.