Abstract:
In this paper, investigation of stationary problems of natural thermal convection in the Boussinesq approximation with irregular boundary data is carried out. Existence and uniqueness theorems for a weak solution of such problems are proved. The smoothness of a weak solution depending on the smoothness of the initial data and the smoothness of the boundary of the domain where the problem is considered is investigated.
Citation:
A. I. Korotkii, D. A. Kovtunov, “On solvability of stationary problems of natural thermal convection of a high-viscosity fluid”, Trudy Inst. Mat. i Mekh. UrO RAN, 14, no. 1, 2008, 61–73; Proc. Steklov Inst. Math. (Suppl.), 261, suppl. 1 (2008), S117–S130
\Bibitem{KorKov08}
\by A.~I.~Korotkii, D.~A.~Kovtunov
\paper On solvability of stationary problems of natural thermal convection of a~high-viscosity fluid
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2008
\vol 14
\issue 1
\pages 61--73
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\elib{https://elibrary.ru/item.asp?id=11929805}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2008
\vol 261
\issue , suppl. 1
\pages S117--S130
\crossref{https://doi.org/10.1134/S0081543808050118}
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Linking options:
https://www.mathnet.ru/eng/timm7
https://www.mathnet.ru/eng/timm/v14/i1/p61
This publication is cited in the following 3 articles:
A. I. Korotkii, D. A. Kovtunov, “Optimal boundary control of a system describing thermal convection”, Proc. Steklov Inst. Math. (Suppl.), 272, suppl. 1 (2011), S74–S100
A. I. Korotkii, “Razreshimost v slabom smysle odnoi kraevoi zadachi, opisyvayuschei teplovuyu konvektsiyu”, Tr. IMM UrO RAN, 16, no. 2, 2010, 121–132
A. I. Korotkii, D. A. Kovtunov, “Optimalnoe upravlenie teplovoi konvektsiei”, Tr. IMM UrO RAN, 16, no. 5, 2010, 103–112
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