Problems on Oscillations of Capillary Fluids and Problems on Hydroelasticity in Immovable Containers

Abstract

This chapter will address two problems that are different in their physical aspects, yet similar in a mathematical sense, because they both are devoted to the study of conservative hydromechanic systems. In Section 4.1, we investigate the problem of small oscillations of a capillary fluid, i.e., a fluid that has surface tension. That tension should be taken into account while considering this problem in conditions close to low-gravity. Further, in Section 4.2, we consider the problem of oscillations of a fluid wholly filling a container with one or two elastic horizontal ends. Finally, in Section 4.3, the problem on oscillations of a fluid partially filling a container with an elastic bottom is formulated and investigated.KeywordsSpectral ProblemSmall OscillationSelfadjoint OperatorCurvilinear Coordinate SystemKinetic Energy OperatorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.