Operator methods in the problem of perturbed motion of a rotating body partially filled with liquid

Abstract

We apply operator methods to the investigation of an initial boundary-value problem which describes the perturbed motion of a body with cavity partially filled with an ideal liquid relative to the uniform rotation of this system about a fixed axis. We prove the existence and uniqueness of generalized solutions with finite energy and establish a sufficient condition for the stability of motion and some properties of the spectrum of the problem under consideration.