On stability and instability of small motions of hydrodynamical systems

Abstract

We give a short survey of an operator approach to some linear evolution and spectral problems of hydrodynamics: small motions and normal oscillations of a heavy or capillary fluid, a partially filled cavity in a moving or immovable vessel. The main attention is given to the problem of stability and instability of these hydromechanical systems with an infinite number of degrees of freedom.