Geodesic
Operator approach to the problem on small motions of an ideal relaxing fluid
Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 64 (2018) no. 3, pp. 459-489

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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 essential and discrete spectrum, and on spectral asymptotics. For nonrotating system in zero-gravity 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. 
@article{CMFD_2018_64_3_a1,
     author = {D. A. Zakora},
     title = {Operator approach to the problem on small motions of an ideal relaxing fluid},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {459--489},
     publisher = {mathdoc},
     volume = {64},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2018_64_3_a1/}
}
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D. A. Zakora. Operator approach to the problem on small motions of an ideal relaxing fluid. Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 64 (2018) no. 3, pp. 459-489. http://geodesic.mathdoc.fr/item/CMFD_2018_64_3_a1/