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 CMFD, 2018, Volume 64, Issue 3, Pages 459–489 (Mi cmfd357)

Operator approach to the problem on small motions of an ideal relaxing fluid

D. A. Zakoraab

a V. I. Vernadsky Crimean Federal University, Simferopol, Russia
b Voronezh State University, Voronezh, Russia

Abstract: 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.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 14.Z50.31.0037

DOI: https://doi.org/10.22363/2413-3639-2018-64-3-459-489

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UDC: 517.9+532

Citation: D. A. Zakora, “Operator approach to the problem on small motions of an ideal relaxing fluid”, Proceedings of the Crimean autumn mathematical school-symposium, CMFD, 64, no. 3, Peoples' Friendship University of Russia, M., 2018, 459–489

Citation in format AMSBIB
\Bibitem{Zak18} \by D.~A.~Zakora \paper Operator approach to the problem on small motions of an ideal relaxing fluid \inbook Proceedings of the Crimean autumn mathematical school-symposium \serial CMFD \yr 2018 \vol 64 \issue 3 \pages 459--489 \publ Peoples' Friendship University of Russia \publaddr M. \mathnet{http://mi.mathnet.ru/cmfd357} \crossref{https://doi.org/10.22363/2413-3639-2018-64-3-459-489}