A boundary value problem for one overdetermined system arising in two-speed hydrodynamics
https://doi.org/10.25587/2411-9326-2023-4-66-80
Abstract
In the half-plane R2+ we consider a stationary system of two-velocity hydrodynamics with one pressure and homogeneous divergent and inhomogeneous boundary conditions for two velocities. Such system is overridden. The solution to this system is reduced to the sequential solution of two boundary value problems: the Stokes problem for one velocity and pressure and an overdetermined boundary value problem for the vector Poisson equation for the other speed. With an appropriate choice of function spaces, the existence and uniqueness are proven for generalized solution with the corresponding stability estimate.
About the Authors
M. V. Urev
Institute of Computational Mathematics and Mathematical Geophysics
Russian Federation
Russian Federation
Mikhail V. Urev
6 Lavrentiev Avenue, Novosibirsk 630090
Kh. Kh. Imomnazarov
Institute of Computational Mathematics and Mathematical Geophysics
Russian Federation
Russian Federation
Kholmatzhon Kh. Imomnazarov
6 Lavrentiev Avenue, Novosibirsk 630090
I. K. Iskandarov
Pacific State University
Russian Federation
Russian Federation
Ilkhom K. Iskandarov
136 Tikhookeanskaya Street, Khabarovsk 680035
S. B. Kuyliev
Samarkand State University
Uzbekistan
Uzbekistan
Sarvar B. Kuyliev
15 Universitetskii Boulevard, Samarkand 140104
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Review
For citations:
Urev M.V., Imomnazarov Kh.Kh., Iskandarov I.K., Kuyliev S.B. A boundary value problem for one overdetermined system arising in two-speed hydrodynamics. Mathematical notes of NEFU. 2023;30(4):66-80. (In Russ.) https://doi.org/10.25587/2411-9326-2023-4-66-80
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