On the existence of vibrations of a cylindrical column of liquid around an elastic core under zero gravity (Q1194566)

The author considers a column of inviscid incompressible liquid under zero gravity around an infinitely long cylindrical isotropic elastic core with an arbitrary cross section and studies the small oscillations of the system, assuming that the motion is parallel to the plane of a cross section. He gives a variational formulation of the problem and, using the methods of functional analysis, proves that, if the volume of the liquid is sufficiently large, the problem can be reduced to a standard vibration problem, so that the existence of the small oscillations is proved.