Mathematical study of the small oscillations of a bubble in a cylindrical liquis column under gravity zero

Thiss paper deals with the mathematical study of the small oscillations of a systems formed by a cylindrical liquid column bounded by two parallel circular disks and an internal spherical bubble constitued by a barotropic gas, under gravity zero. From the equation of motions, the authors deduce a variational equation. Then, the study of the smll oscillations depends on the coerciveness of a hermitian form which appears in this equation. It is proved that this last problem is reduced to an auxiliary eigenvalue problem. A carefull discussion shows that our problem is a classical vibration problem.