Operator Approach to the Problem on Small Motions of an Ideal Relaxing Fluid
Journal: Contemporary Mathematics Fundamental Directions
Year: 2018

In this paper, we study the problem on small motions of an ideal relaxing ﬂuid that ﬁlls a uniformly rotating or ﬁxed container. We prove a theorem on uniform strong solvability of the corresponding initial-boundary value problem. In the case where the system does not rotate, we ﬁnd an asymptotic behavior of the solution under the stress of special form. We investigate the spectral problem associated with the system under consideration. We obtain results on localization of the spectrum, on essen