Mathematical Study of the Small Oscillations of a Spherical Liquid Bridge Between Two Equal Disks Under Gravity Zero

This paper deals with the mathematical study of the problem of small oscillations of a liquid bridge with a free surface, held together by surface tension, between two rigid coaxial disks, under gravity zero, in the case of a spherical liquid bridge in the equilibrium position. The equation which gives the displacement of the free surface, is reduced to a variational equation. After a careful discussion, it can be shown that the bilinear form which appears in the equation, is always coercive. Then, the existence of the eigenfrequencies of the liquid mass can be proved by means of the method of the functional analysis.