AUTHOR(S):

Doretta Vivona, Pierre Capodanno

TITLE

Mathematical analysis of the small oscillations of a bubble in a cylindrical liquid column under gravity zero

ABSTRACT

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

KEYWORDS

Free Boundaries, small oscillations, variational methods.

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Cite this paper

Doretta Vivona, Pierre Capodanno. (2016) Mathematical analysis of the small oscillations of a bubble in a cylindrical liquid column under gravity zero. International Journal of Mathematical and Computational Methods, 1, 92-98

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