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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2021 Volume 61, Number 12, Pages 2125–2132 (Mi zvmmf11336)

Mathematical physics

New mixed variational problem and the Stokes system with a singular right-hand side

M. V. Urevab

a Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia
b Novosibirsk State University, 630090, Novosibirsk, Russia

Abstract: The two-dimensional Stokes problem in a mixed variational statement in a bounded domain with a singular right-hand side given, in particular, by the delta function is considered using an extended scheme for an abstract mixed variational problem. Conditions are established under which a solvability and stability theorem for the solution of a generalized problem of this type is proved.

Key words: two-dimensional Stokes problem, extended mixed statement, singular right-hand side, fractional Sobolev spaces.

UDC: 517.958

Received: 11.11.2020
Revised: 11.11.2020
Accepted: 04.08.2021

DOI: 10.31857/S0044466921120152


 English version:
Computational Mathematics and Mathematical Physics, 2021, 61:12, 2129–2136

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© Steklov Math. Inst. of RAS, 2026