Operator Approach to the Problem on Small Motions of an Ideal Relaxing Fluid

Abstract

In this paper, we study the problem on small motions of the ideal relaxing fluid that fills a uniformly rotating or fixed container. We prove a theorem on the uniform strong solvability of the corresponding initial-boundary problem. In the case where the system does not rotate, we find the asymptotic behavior of the solution under the stress of a special form. We investigate the spectral problem associated with the considered system. We obtain localization results for the spectrum, results on the essential and discrete spectrum, and results on asymptotic properties of the spectrum. For the nonrotating system in the weightlessness conditions, we prove the multiple basis property of a special system of elements. In this case, we find an expansion of the solution of the evolution problem in the special system of elements.